PATENT ABSTRACT
A method for a base station to receive a reference signal sequence from one or more devices within a cell of the base station in a multiple cell environment includes providing the one or more devices with information about the reference signal sequence, wherein the reference signal sequence is defined by a cyclic shift of a base sequence, wherein the base sequence is one of a plurality of base sequences divided into groups, wherein each of the groups comprises at least one base sequence for each length (N), wherein each length (N) corresponds to (12*n), (n) being a positive integer, and receiving the reference signal sequence from one or more of the one or more devices.

PATENT DESCRIPTION
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. application Ser. No. 12/024,884, filed Feb. 1, 2008, currently pending, which pursuant to 35 U.S.C. §119 claims the benefit of Korean Patent Application Nos. 10-2007-0047494, filed on May 16, 2007, 10-2007-0099707, filed on Oct. 4, 2007, 10-2007-0108226, filed on Oct. 26, 2007 and 10-2007-0109089, filed on Oct. 29, 2007, and U.S. Provisional Application Ser. Nos. 60/888,065, filed on Feb. 2, 2007, 60/984,386, filed on Nov. 1, 2007 and 61/019,588, filed on Jan. 7, 2008, the contents of which are hereby incorporated by reference herein in their entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to method for generating a reference signal sequence, and more particularly, to a method for grouping sequences having a variable length corresponding one or multiple of a resource block size, a method for generating a reference signal sequence and a method for generating a reference signal sequence using Zadoff-Chu (ZC) sequence. 
         [0004]    2. Discussion of the Related Art 
         [0005]    Following explanation is mainly discussed in view of 3GPP LTE system, but the present invention is not limited to this system, and exemplary 3GPP LTE system is only for making those skilled in the art clearly understand the present invention. 
         [0006]    There are a lot of sequences used for transmitting signal, but in 3GPP LTE (3 rd  Generation Partnership Project Long Term Evolution) system, CAZAC (Constant Amplitude Zero Auto-Correlation) sequence forms the basis sequence for transmitting signals. CAZAC sequence can be used to various channels for extracting ID or control information, such as uplink/downlink synchronization channels (SCH) including P-SCH (primary SCH) and S-SCH (Secondary SCH), pilot channel for transmitting reference signal. And, the CAZAC sequence can be used in scrambling. 
         [0007]    Two types of CAZAC sequences, i.e., GCL CAZAC sequence and Zadoff-Chu CAZAC sequence are mainly used as the CAZAC sequences. The two types of CAZAC sequences are associated with each other by a conjugate complex relation. That is, the GCL CAZAC sequence can be acquired by conjugate complex calculation for the Zadoff-Chu CAZAC sequence. The Zadoff-Chu CAZAC sequence is given as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     c 
                      
                     
                       ( 
                       
                         
                           k 
                           ; 
                           N 
                         
                         , 
                         M 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       exp 
                        
                       
                         ( 
                         
                           
                             jπ 
                              
                             
                                 
                             
                              
                             
                               Mk 
                                
                               
                                 ( 
                                 
                                   k 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           N 
                         
                         ) 
                       
                     
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         for 
                          
                         
                             
                         
                          
                         odd 
                          
                         
                             
                         
                          
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     c 
                      
                     
                       ( 
                       
                         
                           k 
                           ; 
                           N 
                         
                         , 
                         M 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       exp 
                        
                       
                         ( 
                         
                           
                             jπ 
                              
                             
                                 
                             
                              
                             
                               Mk 
                               2 
                             
                           
                           N 
                         
                         ) 
                       
                     
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         for 
                          
                         
                             
                         
                          
                         even 
                          
                         
                             
                         
                          
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
         [0008]    where k represents a sequence component index, N represents a length of CAZAC sequence to be generated, and M represents, sequence ID or sequence index. 
         [0009]    When the Zadoff-Chu CAZAC sequence given by the Equations 1 and 2 and the GCL CAZAC sequence which is a conjugate complex relation with the Zadoff-Chu CAZAC sequence are represented by c(k;N,M), these sequence can have three features as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     
                       C 
                        
                       
                         ( 
                         
                           k 
                           ; 
                           N 
                           ; 
                           M 
                         
                         ) 
                       
                     
                      
                   
                   = 
                   
                     1 
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           for 
                            
                           
                               
                           
                            
                           all 
                            
                           
                               
                           
                            
                           k 
                         
                         , 
                         N 
                         , 
                         M 
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       R 
                       
                         M 
                         · 
                         N 
                       
                     
                      
                     
                       ( 
                       d 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             1 
                             , 
                           
                         
                         
                           
                             ( 
                             
                               
                                 for 
                                  
                                 
                                     
                                 
                                  
                                 d 
                               
                               = 
                               0 
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           
                             ( 
                             
                               
                                 for 
                                  
                                 
                                     
                                 
                                  
                                 d 
                               
                               ≠ 
                               0 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       R 
                       
                         
                           M 
                            
                           
                               
                           
                            
                           1 
                         
                         , 
                         
                           
                             M 
                              
                             
                                 
                             
                              
                             2 
                           
                           ; 
                           N 
                         
                       
                     
                      
                     
                       ( 
                       d 
                       ) 
                     
                   
                   = 
                   
                     p 
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           for 
                            
                           
                               
                           
                            
                           all 
                            
                           
                               
                           
                            
                           
                             M 
                             1 
                           
                         
                         , 
                         
                           
                             M 
                             2 
                           
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           N 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
         [0010]    The Equation 3 means that the CAZAC sequence always has a size of 1, and the Equation 4 shows that an auto-correlation function of the CAZAC sequence is expressed by a delta function. In this case, the auto-correlation is based on circular correlation. Also, the Equation 5 shows that a cross-correlation is always a constant. 
         [0011]    Among these two kinds of CAZAC sequence, the following explanation is mainly focused on the Zadoff Chu sequence (hereinafter “ZC sequence”). 
         [0012]    In the 3GPP LTE system, using this ZC sequence as reference signal sequence, the length of the ZC sequence should be equal to the resource block size. And, not only using one resource block size sequence, but the reference signal sequence having the length corresponding to multiples of resource block size can be used. 
         [0013]    For a single-cell environment, the reference signals are transmitted by the localized FDM (Frequency Divisional Multiplexing) method for multiplexing signals from multiple user equipments (UEs). But, for the multi-cell environment, the reference signals are transmitted by the additional CDM (Code Divisional Multiplexing) method for distinguishing the signals from that of the neighboring cells. In this multiplexing, two type of method is possible. One is a CDM method using a ZC sequence having a different root indexes, and the other is a CDM method using a ZC sequence having the same root index (M) and but having differently applied cyclic shift. 
         [0014]    When the length of the reference signals using these kinds of ZC sequences is same, the cross correlation values for both of the cases are not large. But, when the reference signals having a difference length came as interference from the neighboring cells and transmitted through the same frequency band or overlapped frequency band, the cross correlation value would be significant. 
       SUMMARY OF THE INVENTION 
       [0015]    Accordingly, the present invention is directed to provide a method for generating reference signal sequence, which minimizes the interference caused by the signals having different length, came from the neighboring cells. 
         [0016]    For this method, the present invention also provides a method for effectively grouping sequences such that each of the group is consisted of the sequences having high cross correlation value, and supports variable length sequences to be used as a reference signals. 
         [0017]    Also, the present invention provides a method for generating reference signal sequence based on the above grouping. 
         [0018]    To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method for grouping sequences having a variable length corresponding one or multiple of a resource block size is provided. According to one embodiment, the method comprises: grouping the sequences into groups such that each of the groups contains at least one sequence of each length, wherein the grouped sequence is a base sequence which is used for applying a cyclic shift corresponding to variable cyclic shift value, and the base sequence with the cyclic shift is used as a reference signal sequence. 
         [0019]    Preferably, a number of the groups is 30. 
         [0020]    And, said grouping may be performed such that each of the groups contains one base sequence of each length corresponding to 1 to 5 times of the resource block size, and two base sequences of each length corresponding to 6 or more times of the resource block size. 
         [0021]    And, preferably, the base sequence having a length corresponding to 3 or more times of the resource block size is defined by using a Zadoff-Chu (ZC) sequence, and the base sequence having a length corresponding to 1 or 2 times of the resource block size is defined by using other sequence other than the ZC sequence. 
         [0022]    In another aspect of the present invention, a method for generating a reference signal sequence is provided. In one embodiment for this aspect, the method comprises: defining one or more base sequences having a variable length corresponding to one or multiple of a resource block size; and applying a cyclic shift corresponding to variable cyclic shift value to the defined base sequence, wherein the base sequences are divided into groups, and each of the group comprises at least one base sequence of each length. 
         [0023]    In this case, the base sequence may be defined by cyclic extension of the ZC sequence having a length (N zc   RS ) given by a largest prime number which is less than a corresponding reference signal sequence size. Also the base sequence may be defined by truncation of the ZC sequence having a length (N zc   RS ) given by the smallest prime number which is larger than a corresponding reference signal sequence size. 
         [0024]    Also in this embodiment, preferably, a number of the groups is 30. 
         [0025]    And, each of the groups may contain one base sequence of each length corresponding to 1 to 5 times of the resource block size, and two base sequences of each length corresponding to 6 or more times of the resource block size. 
         [0026]    And, the base sequence having a length corresponding to 3 or more times of the resource block size may be defined by using a Zadoff-Chu (ZC) sequence with specific ZC sequence index (q), and the base sequence having a length corresponding to 1 or 2 times of the resource block size may be defined by using other sequence other than the ZC sequence. 
         [0027]    And, preferably, the specific ZC sequence index (q) is a function of a group index (u) and a base sequence number index (v) within the group. 
         [0028]    And, the defined base sequence with cyclic shift may be used for uplink reference signal sequence. 
         [0029]    Also for above embodiments, the resource block size may correspond to a size of 12 subcarriers in a frequency domain. 
         [0030]    In another aspect of the present invention, a method for generating a reference signal sequence using Zadoff-Chu (ZC) sequence is provided. In on embodiment for this aspect, the method comprises: defining a specific base sequence using q-th root ZC sequence, wherein the base sequences are divided into groups, and the “q” is a function of a group index (u) and a base sequence number index (v) within the group; and applying a cyclic shift corresponding to variable cyclic shift value to the defined base sequence to generate the reference signal sequence. 
         [0031]    In one case, the specific ZC sequence index (q) may be determined by one of equations of, 
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         
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                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
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                             ( 
                             
                               - 
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                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
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                           · 
                           
                             ( 
                             
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                               + 
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                             ) 
                           
                         
                         
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                             , 
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                           RS 
                         
                       
                     
                     , 
                     
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                       ∈ 
                       
                         { 
                         
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                           , 
                           1 
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                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
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                             1 
                           
                         
                         } 
                       
                     
                     , 
                   
                 
               
               
                 
                   ( 
                   1 
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                     = 
                     
                       
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                          
                         
                           ( 
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                       + 
                       
                         
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                         where 
                          
                         
                             
                         
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                           - 
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                         { 
                         
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                           , 
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                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
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                                
                               
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                                     RS 
                                   
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                         } 
                       
                     
                     , 
                     or 
                   
                 
               
               
                 
                   ( 
                   2 
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                     = 
                     
                       
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                          
                         
                           ( 
                           y 
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                    
                   
                     
 
                   
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                         where 
                          
                         
                             
                         
                          
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                       = 
                       
                         
                           round 
                           ( 
                           
                             
                               N 
                               zc 
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                                 reference 
                                 , 
                                 zc 
                               
                               RS 
                             
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
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                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         
                           { 
                           
                             0 
                             , 
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                              
                             
                                 
                             
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                                  
                                 
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                                       RS 
                                     
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                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0032]    wherein N zc   RS  is the length given by the largest prime number which is less than the corresponding reference signal sequence size, N reference,zc   RS  is the corresponding reference signal sequence size, the “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. But, N zc   RS  can be the length given by the smallest prime number which is greater than the corresponding reference signal sequence, for another embodiment of this invention. 
         [0033]    In the other case, the specific ZC sequence index (q) may be determined by one of equations of, 
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
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                             + 
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                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
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                             ( 
                             
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                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
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                            
                           
                               
                           
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                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
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                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
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                     = 
                     
                       
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                          
                         
                           ( 
                           
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                             + 
                             
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                                
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                                
                               
                                 ( 
                                 
                                   
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                                      
                                     
                                       ( 
                                       
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                                         + 
                                         0.5 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
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                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               - 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
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                             ) 
                           
                         
                         
                           
                             N 
                             
                               reference 
                               , 
                               zc 
                             
                             RS 
                           
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
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                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
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                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     , 
                     or 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
                                 1 
                               
                               2 
                             
                             ) 
                           
                         
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     floor 
                                      
                                     
                                       ( 
                                       
                                         y 
                                         + 
                                         0.5 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
                             + 
                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           floor 
                           ( 
                           
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               
                                 N 
                                 
                                   reference 
                                   , 
                                   zc 
                                 
                                 RS 
                               
                             
                             + 
                             0.5 
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               
                                 floor 
                                  
                                 
                                   ( 
                                   
                                     
                                       N 
                                       ZC 
                                       RS 
                                     
                                     / 
                                     30 
                                   
                                   ) 
                                 
                               
                               - 
                               1 
                             
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0034]    wherein N zc   RS  is the length given by the largest prime number which is less than the corresponding reference signal sequence size, N reference,zc   RS  is the corresponding reference signal sequence size, the “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. But, N zc   RS  can be the length given by the smallest prime number which is greater than the corresponding reference signal sequence, for another embodiment of this invention. 
         [0035]    In one specific embodiment of this invention, the maximum number of the base sequence number index (v) within each group may be set to is 2, and then the specific ZC sequence index (q) can be determined by one of equations of, 
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           N 
                           
                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               - 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             N 
                             
                               reference 
                               , 
                               zc 
                             
                             RS 
                           
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                     , 
                     or 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           round 
                           ( 
                           
                             
                               N 
                               zc 
                               RS 
                             
                             
                               N 
                               
                                 reference 
                                 , 
                                 zc 
                               
                               RS 
                             
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         
                           { 
                           
                             0 
                             , 
                             1 
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0036]    rr by one of equations of, 
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           N 
                           
                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               - 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             N 
                             
                               reference 
                               , 
                               zc 
                             
                             RS 
                           
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                     , 
                     or 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           floor 
                           ( 
                           
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               
                                 N 
                                 
                                   reference 
                                   , 
                                   zc 
                                 
                                 RS 
                               
                             
                             + 
                             0.5 
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         
                           { 
                           
                             0 
                             , 
                             1 
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0037]    Preferably, N reference,zc   RS  can be set to 31 or 37, but N reference,zc   RS  can be set to other values as well. 
         [0038]    According to these embodiments of this invention, because the base sequence for applying cyclic shift is grouped, and each group contains at least one base sequence of each length, UE(s) can use various length sequences as a reference signal sequence when specific group is allocated to one cell or Node B. 
         [0039]    Additionally, because each group contains base sequences having high cross correlation relation, if each group is allocated to one cell or Node B, inter cell interference can be minimized. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0040]    The accompanying drawings, which are included to provide a further understanding of the invention, illustrate embodiments of the invention and together with the description serve to explain the principle of the invention. 
           [0041]    In the drawings: 
           [0042]      FIG. 1  shows a conceptual diagram for explaining the truncated sequence generation method. 
           [0043]      FIG. 2  shows a conceptual diagram for explaining the generation method using padding part. 
           [0044]      FIGS. 3 to 5  show conceptual diagrams of grouping sequences according to one embodiment of this invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0045]    Hereinafter, the preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It is to be understood that the detailed description which will be disclosed along with the accompanying drawings is intended to describe the exemplary embodiments of the present invention, and is not intended to describe a unique embodiment which the present invention can be carried out. 
         [0046]    Hereinafter, the detailed description includes detailed matters to provide full understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention can be carried out without the detailed matters. To prevent the concept of the present invention from being ambiguous, structures and apparatuses of the known art will be omitted, or will be shown in the form of a block diagram based on main functions of each structure and apparatus. Also, wherever possible, the same reference numbers will be used throughout the drawings and the specification to refer to the same or like parts. 
         [0047]    As stated above, the present invention is directed to provide a method for generating reference signal sequence, which minimizes the interference caused by the signals having different length, came from the neighboring cells. 
         [0048]    To this end, the length of the CAZAC sequence is explained. 
         [0049]    Presently, in the 3GPP LTE system, the resource block (RB) size for transmitting all kind of the OFDM symbol including reference signal symbol corresponds to the size of 12 subcarriers. So, when ZC is generated for uplink reference signal sequence, the size of ZC sequence would correspond to 12 subcarriers size. 
         [0050]    For the case of CAZAC sequence, the number of CAZAC sequence indexes (M) which could be distinguished from each other is decided by the number of relative prime number relative prime to the sequence length (N). So, when the ZC sequence is generated to have the length of 12, the number of ZC sequences having a different sequence index is 4. But, if the ZC sequence is generated based on the prime number length (N), the number of ZC sequence having a different sequence index can be N−1, which maximizes the number of ZC sequence. Therefore, various methods for generating CAZAC sequence based on the prime number length are provided. 
         [0051]    First, a truncated sequence generation method is explained. 
         [0052]      FIG. 1  shows a conceptual diagram for explaining the truncated sequence generation method. 
         [0053]    As shown in the  FIG. 1 , when the required CAZAC sequence length is “L”, CAZAC sequence having the prime number length of “X” (where X&gt;L) is generated. And, the generated CAZAC sequence having the length “X” is truncated to have the length “L”, that is, part of the sequence having the length of “X−L” is truncated. 
         [0054]    By this method, the number of CAZAC sequence is maximized. But because part of the generated sequence is truncated, the auto/cross correlation properties of CAZAC sequence explained with the equations 4 and 5 are somewhat deteriorated. And, when the sequences having poor correlation properties are eliminated, the actual number of sequence is diminished. Moreover, because of the truncation, good PAPR property of CAZAC sequence can also be deteriorated. 
         [0055]    So, another type of methods for generating CAZAC sequence based on the prime number is presented. One of these method is that the CAZAC sequence is generated to have the prime number length “X” (where X&lt;L), and components having the length of “L−X” is added to the generated CAZAC sequence. This components added to the generated sequence can be called as padding part, so this method can be called as generation method using padding part. 
         [0056]      FIG. 2  shows a conceptual diagram for explaining the generation method using padding part. 
         [0057]    As shown in the  FIG. 2 , when the required CAZAC sequence length is “L”, the CAZAC sequence is generated to have the length “X”, which is a maximum prime number smaller than “L”. And, the padding part having the length of “L−X” is added to the generated sequence. 
         [0058]    In one method for this kind of methods, the padding part can be consisted of zeros. By this method, the number of CAZAC sequence can be maximized. Moreover, the auto/cross correlation properties of the CAZAC sequence can be maintained when distinction of the sequences is done with regard to the length of “C 1 ” in  FIG. 2 . 
         [0059]    And, preferably, the padding part can be a cyclic extension of the CAZAC sequence. That is, the padding part (C 2 ) can be generated by cyclic copying of the first part of the generated CAZAC sequence, and be added to the generated sequence. By doing so, the resultant sequence can have a good auto-cross correlation propertied even when the distinction of the sequence is done with regard to the entire sequence length (L). So, this method has further advantage than the above method using the padding part as zeros. 
         [0060]    The present invention for generating reference signal sequence using CAZAC sequence is mainly based on the generation method using padding part generated by the above mentioned cyclic extension. But, limitation to this generation method is not necessary, that is, present invention can be based on the truncated sequence generation method and the generation method using padding part consisted of zeros. 
         [0061]    Based on this, the inter cell interference caused by using sequences having difference length is explained. 
         [0062]    When CAZAC sequence is used for reference signal sequence, the inter cell interference is proportional to the cross correlation value between two sequence. So, in the following examples, the cross correlation value, caused by the overlapping between the original reference signal transmitted through certain resource region and the incoming sequence came from the neighboring cells, having difference length from that of the original reference signal, and transmitted through the same resource region, is considered with regard to the index of the ZC sequences. 
         [0063]    More specifically, in the following examples, the sequences having the length of 1 RB, 2 RB and 3 RB is considered. And, let us presume that the sequences having the length of 1 RB and 2 RB are generated by the cyclic extension of the ZC sequence having the length given by the largest prime number which is less than a corresponding resource block size. And, let us presume that the sequence having the length of 3 RB is generated by the truncated sequence generation method. That is, the sequences can be generated to have the corresponding resource block size based on the prime number length by one of the above 3 generation methods. 
         [0064]    First, consider the case when the sequence having 1 RB length and the sequence having 2 RB length is overlapped in the same resource region. The sequence having 1 RB length and the sequence having 2 RB length can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           g 
                           
                             1 
                              
                             RB 
                           
                         
                          
                         
                           ( 
                           
                             k 
                             ; 
                             
                               s 
                               1 
                             
                           
                           ) 
                         
                       
                       = 
                       
                          
                         
                           
                             - 
                             j 
                           
                            
                           
                             π 
                             
                               N 
                               1 
                             
                           
                            
                           
                             s 
                             1 
                           
                            
                           
                             k 
                              
                             
                               ( 
                               
                                 k 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       k 
                       = 
                       0 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       N 
                       - 
                       1 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           g 
                           
                             2 
                              
                             RB 
                           
                         
                          
                         
                           ( 
                           
                             k 
                             ; 
                             
                               s 
                               2 
                             
                           
                           ) 
                         
                       
                       = 
                       
                          
                         
                           
                             - 
                             j 
                           
                            
                           
                             π 
                             
                               N 
                               2 
                             
                           
                            
                           
                             s 
                             2 
                           
                            
                           
                             k 
                              
                             
                               ( 
                               
                                 k 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       k 
                       = 
                       0 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         2 
                          
                         N 
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
         [0065]    Here, s 1  and s 2  indicate the indexes which are relative prime to the sequence length (N or 2N). In this example, for the sequences having 1 RB length and 2 RB length are generated using the cyclic extension method, s 1  can be 1, 2, . . . , 10 and s 2  can be 1, 2, . . . , 22. And, N 1  may be 11, and N 2  may be 23. 
         [0066]    Based on this, the cross correlation value c(d;s 1 ,s 2 )) generated when the sequence with 1 RB length is overlapped with the sequence with 2 RB length in the first 12 subcarriers region of the sequence with 2 RB length can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       c 
                        
                       
                         ( 
                         
                           
                             d 
                             ; 
                             
                               s 
                               1 
                             
                           
                           , 
                           
                             s 
                             2 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           
                             g 
                             
                               1 
                                
                               RB 
                             
                           
                            
                           
                             ( 
                             
                               k 
                               ; 
                               
                                 s 
                                 1 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                             g 
                             
                               2 
                                
                               RB 
                             
                             * 
                           
                            
                           
                             ( 
                             
                               
                                 k 
                                 + 
                                 d 
                               
                               ; 
                               
                                 s 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         For 
                          
                         
                             
                         
                          
                         d 
                       
                       = 
                       0 
                     
                     , 
                     
                       
 
                     
                      
                     
                       
                         
                           
                             
                               c 
                                
                               
                                 ( 
                                 
                                   
                                     0 
                                     ; 
                                     
                                       s 
                                       1 
                                     
                                   
                                   , 
                                   
                                     s 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             = 
                               
                              
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     
                                       - 
                                       j 
                                     
                                      
                                     
                                       π 
                                       
                                         N 
                                         1 
                                       
                                     
                                      
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       mod 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           , 
                                           
                                             N 
                                             - 
                                             1 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           mod 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               , 
                                               
                                                 N 
                                                 - 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                     π 
                                     
                                       N 
                                       2 
                                     
                                   
                                    
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     mod 
                                      
                                     
                                       ( 
                                       
                                         k 
                                         , 
                                         
                                           
                                             2 
                                              
                                             N 
                                           
                                           - 
                                           1 
                                         
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         mod 
                                          
                                         
                                           ( 
                                           
                                             k 
                                             , 
                                             
                                               
                                                 2 
                                                  
                                                 N 
                                               
                                               - 
                                               1 
                                             
                                           
                                           ) 
                                         
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                               
                              
                             
                               
                                 [ 
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       0 
                                     
                                     10 
                                   
                                    
                                   
                                     exp 
                                      
                                     
                                       { 
                                       
                                         jπ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           k 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               + 
                                               1 
                                             
                                             ) 
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               
                                                 s 
                                                 2 
                                               
                                               23 
                                             
                                             - 
                                             
                                               
                                                 s 
                                                 1 
                                               
                                               11 
                                             
                                           
                                           ) 
                                         
                                       
                                       } 
                                     
                                   
                                 
                                 ] 
                               
                               + 
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     j 
                                      
                                     
                                       π 
                                       23 
                                     
                                      
                                     
                                       
                                         s 
                                         2 
                                       
                                       · 
                                       11 
                                       · 
                                       12 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
         [0067]    According to the equation 7, it can be understood that if the combination of sequence indexes (s 1  and s 2 ) meet the condition that the term of 
         [0000]    
       
         
           
             ( 
             
               
                 
                   s 
                   2 
                 
                 23 
               
               - 
               
                 
                   s 
                   1 
                 
                 11 
               
             
             ) 
           
         
       
     
         [0000]    becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. 
         [0068]    Therefore, one embodiment of the present invention proposes to perform grouping the sequences into groups such that the sequences contained in each group have the high cross correlation relation with each other. And, if 1 RB length sequence and 2 RB length sequence are considered, grouping the combination of sequence indexes which meets the condition that the term of 
         [0000]    
       
         
           
             ( 
             
               
                 
                   s 
                   2 
                 
                 23 
               
               - 
               
                 
                   s 
                   1 
                 
                 11 
               
             
             ) 
           
         
       
     
         [0000]    becomes close to zero is proposed. 
         [0069]    But, to determine more general condition for the grouping sequences, let us consider some other examples. 
         [0070]    When 1 RB sequence is overlapped in the last 12 subcarriers region of the 2 RB sequence, the cross correlation value (c(d;s 1 ,s 2 )) of the two sequences can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         c 
                          
                         
                           ( 
                           
                             
                               d 
                               ; 
                               
                                 s 
                                 1 
                               
                             
                             , 
                             
                               s 
                               2 
                             
                           
                           ) 
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           
                             N 
                             - 
                             1 
                           
                         
                          
                         
                           
                             
                               g 
                               
                                 1 
                                  
                                 RB 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 ; 
                                 
                                   s 
                                   1 
                                 
                               
                               ) 
                             
                           
                            
                           
                             
                               g 
                               
                                 2 
                                  
                                 RB 
                               
                               * 
                             
                              
                             
                               ( 
                               
                                 
                                   k 
                                   + 
                                   12 
                                   + 
                                   d 
                                 
                                 ; 
                                 
                                   s 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           For 
                            
                           
                               
                           
                            
                           d 
                         
                         = 
                         0 
                       
                       , 
                       
                         
 
                       
                        
                       
                         
                           
                             
                               
                                 c 
                                  
                                 
                                   ( 
                                   
                                     
                                       d 
                                       ; 
                                       
                                         s 
                                         1 
                                       
                                     
                                     , 
                                     
                                       s 
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                               = 
                                 
                                
                               
                                 
                                   ∑ 
                                   
                                     k 
                                     = 
                                     0 
                                   
                                   
                                     N 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   exp 
                                    
                                   
                                     ( 
                                     
                                       
                                         - 
                                         j 
                                       
                                        
                                       
                                         π 
                                         
                                           N 
                                           1 
                                         
                                       
                                        
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         mod 
                                          
                                         
                                           ( 
                                           
                                             k 
                                             , 
                                             
                                               N 
                                               - 
                                               1 
                                             
                                           
                                           ) 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             mod 
                                              
                                             
                                               ( 
                                               
                                                 k 
                                                 , 
                                                 
                                                   N 
                                                   - 
                                                   1 
                                                 
                                               
                                               ) 
                                             
                                           
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                                 
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     j 
                                      
                                     
                                       π 
                                       
                                         N 
                                         2 
                                       
                                     
                                      
                                     
                                       s 
                                       2 
                                     
                                      
                                     
                                       mod 
                                        
                                       
                                         ( 
                                         
                                           
                                             k 
                                             + 
                                             12 
                                           
                                           , 
                                           
                                             
                                               2 
                                                
                                               N 
                                             
                                             - 
                                             1 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           mod 
                                            
                                           
                                             ( 
                                             
                                               
                                                 k 
                                                 + 
                                                 12 
                                               
                                               , 
                                               
                                                 
                                                   2 
                                                    
                                                   N 
                                                 
                                                 - 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               = 
                                 
                                
                               
                                 
                                   [ 
                                   
                                     
                                       ∑ 
                                       
                                         k 
                                         = 
                                         0 
                                       
                                       10 
                                     
                                      
                                     
                                       exp 
                                        
                                       
                                         { 
                                         
                                           
                                             jπ 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               k 
                                                
                                               
                                                 ( 
                                                 
                                                   k 
                                                   + 
                                                   1 
                                                 
                                                 ) 
                                               
                                             
                                              
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     s 
                                                     2 
                                                   
                                                   23 
                                                 
                                                 - 
                                                 
                                                   
                                                     s 
                                                     1 
                                                   
                                                   11 
                                                 
                                               
                                               ) 
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 s 
                                                 2 
                                               
                                               23 
                                             
                                             · 
                                             12 
                                             · 
                                             
                                               ( 
                                               
                                                 
                                                   2 
                                                    
                                                   k 
                                                 
                                                 + 
                                                 13 
                                               
                                               ) 
                                             
                                           
                                         
                                         } 
                                       
                                     
                                   
                                   ] 
                                 
                                 + 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
         [0071]    According to the equation 8, it can also concluded that if the combination of sequence indexes (s 1  and s 2 ) meet the condition that the term of 
         [0000]    
       
         
           
             ( 
             
               
                 
                   s 
                   2 
                 
                 23 
               
               - 
               
                 
                   s 
                   1 
                 
                 11 
               
             
             ) 
           
         
       
     
         [0000]    becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. So, if 1 RB length sequence and 2 RB length sequence are considered, the position where the overlapping is occurred is not change the grouping condition. 
         [0072]    Next, let us consider the case when the 1 RB length sequence and the 3 RB length sequence are overlapped in the same resource region. 
         [0073]    First of all, the 1 RB length sequence and the 3 RB length sequence can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           g 
                           
                             1 
                              
                             RB 
                           
                         
                          
                         
                           ( 
                           
                             k 
                             ; 
                             
                               s 
                               1 
                             
                           
                           ) 
                         
                       
                       = 
                       
                          
                         
                           
                             - 
                             j 
                           
                            
                           
                             π 
                             
                               N 
                               1 
                             
                           
                            
                           
                             s 
                             1 
                           
                            
                           
                             k 
                              
                             
                               ( 
                               
                                 k 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       k 
                       = 
                       0 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       N 
                       - 
                       1 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           g 
                           
                             3 
                              
                             RB 
                           
                         
                          
                         
                           ( 
                           
                             k 
                             ; 
                             
                               s 
                               3 
                             
                           
                           ) 
                         
                       
                       = 
                       
                          
                         
                           
                             - 
                             j 
                           
                            
                           
                             π 
                             
                               N 
                               3 
                             
                           
                            
                           
                             s 
                             3 
                           
                            
                           
                             k 
                              
                             
                               ( 
                               
                                 k 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       k 
                       = 
                       0 
                     
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         3 
                          
                         N 
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
         [0074]    Here, s 1  and s 3  indicate the indexes which are relative prime to the sequence length (N or 3N). In this example, for the 1 RB length sequences is generated using the cyclic extension method and the 3 RB length sequence is generated using the truncated sequence generation method, s 1  can be 1, 2, . . . , 10 and s 2  can be 1, 2, . . . , 36. And, N 1  may be 11, and N 2  may be 37. 
         [0075]    Based on this, if the 1 RB length sequence is overlapped in the first 12 subcarriers region of the 3 RB length sequence, the cross correlation value between the two sequences can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       c 
                        
                       
                         ( 
                         
                           
                             d 
                             ; 
                             
                               s 
                               1 
                             
                           
                           , 
                           
                             s 
                             3 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           
                             g 
                             
                               1 
                               , 
                               RB 
                             
                           
                            
                           
                             ( 
                             
                               k 
                               ; 
                               
                                 s 
                                 1 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                             g 
                             
                               3 
                                
                               RB 
                             
                             * 
                           
                            
                           
                             ( 
                             
                               
                                 k 
                                 + 
                                 d 
                               
                               ; 
                               
                                 s 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         For 
                          
                         
                             
                         
                          
                         d 
                       
                       = 
                       0 
                     
                     , 
                     
                       
 
                     
                      
                     
                       
                         
                           
                             
                               c 
                                
                               
                                 ( 
                                 
                                   
                                     0 
                                     ; 
                                     
                                       s 
                                       1 
                                     
                                   
                                   , 
                                   
                                     s 
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             = 
                               
                              
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     
                                       - 
                                       j 
                                     
                                      
                                     
                                       π 
                                       
                                         N 
                                         1 
                                       
                                     
                                      
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       mod 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           , 
                                           
                                             N 
                                             - 
                                             1 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           mod 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               , 
                                               
                                                 N 
                                                 - 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                     π 
                                     
                                       N 
                                       3 
                                     
                                   
                                    
                                   
                                     s 
                                     3 
                                   
                                    
                                   
                                     k 
                                      
                                     
                                       ( 
                                       
                                         k 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                               
                              
                             
                               
                                 [ 
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       0 
                                     
                                     10 
                                   
                                    
                                   
                                     exp 
                                      
                                     
                                       { 
                                       
                                         jπ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           k 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               + 
                                               1 
                                             
                                             ) 
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               
                                                 s 
                                                 3 
                                               
                                               37 
                                             
                                             - 
                                             
                                               
                                                 s 
                                                 1 
                                               
                                               11 
                                             
                                           
                                           ) 
                                         
                                       
                                       } 
                                     
                                   
                                 
                                 ] 
                               
                               + 
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     j 
                                      
                                     
                                       π 
                                       37 
                                     
                                      
                                     
                                       
                                         s 
                                         3 
                                       
                                       · 
                                       11 
                                       · 
                                       12 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
         [0076]    According to the equation 10, it can be understood that if the combination of sequence indexes (s 1  and s 3 ) meet the condition that the term of 
         [0000]    
       
         
           
             ( 
             
               
                 
                   s 
                   3 
                 
                 37 
               
               - 
               
                 
                   s 
                   1 
                 
                 11 
               
             
             ) 
           
         
       
     
         [0000]    becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. Therefore, if 1 RB length sequence and 3 RB length sequence are considered, grouping the combination of sequence indexes which meets the condition that the term of 
         [0000]    
       
         
           
             ( 
             
               
                 
                   s 
                   3 
                 
                 37 
               
               - 
               
                 
                   s 
                   1 
                 
                 11 
               
             
             ) 
           
         
       
     
         [0000]    becomes close to zero is proposed. 
         [0077]    And, to certify the relation with the position where the overlapping is occurred, let us consider the case when the 1 RB length sequence is overlapped in the second  12  subcarriers region of the 3 RB length sequence. In this case, the cross correlation value between these two sequences can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       c 
                        
                       
                         ( 
                         
                           
                             d 
                             ; 
                             
                               s 
                               1 
                             
                           
                           , 
                           
                             s 
                             3 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           
                             g 
                             
                               1 
                                
                               RB 
                             
                           
                            
                           
                             ( 
                             
                               k 
                               ; 
                               
                                 s 
                                 1 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                             g 
                             
                               3 
                                
                               RB 
                             
                             * 
                           
                            
                           
                             ( 
                             
                               
                                 k 
                                 + 
                                 12 
                                 + 
                                 d 
                               
                               ; 
                               
                                 s 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         For 
                          
                         
                             
                         
                          
                         d 
                       
                       = 
                       0 
                     
                     , 
                     
                       
 
                     
                      
                     
                       
                         
                           
                             
                               c 
                                
                               
                                 ( 
                                 
                                   
                                     0 
                                     ; 
                                     
                                       s 
                                       1 
                                     
                                   
                                   , 
                                   
                                     s 
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             = 
                               
                              
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     
                                       - 
                                       j 
                                     
                                      
                                     
                                       π 
                                       
                                         N 
                                         1 
                                       
                                     
                                      
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       mod 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           , 
                                           
                                             N 
                                             - 
                                             1 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           mod 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               , 
                                               
                                                 N 
                                                 - 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                     π 
                                     
                                       N 
                                       3 
                                     
                                   
                                    
                                   
                                     
                                       s 
                                       3 
                                     
                                      
                                     
                                       ( 
                                       
                                         k 
                                         + 
                                         12 
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       + 
                                       13 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                               
                              
                             
                               
                                 [ 
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       0 
                                     
                                     10 
                                   
                                    
                                   
                                     exp 
                                      
                                     
                                       [ 
                                       
                                         jπ 
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 k 
                                                  
                                                 
                                                   ( 
                                                   
                                                     k 
                                                     + 
                                                     1 
                                                   
                                                   ) 
                                                 
                                               
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     
                                                       s 
                                                       3 
                                                     
                                                     37 
                                                   
                                                   - 
                                                   
                                                     
                                                       s 
                                                       1 
                                                     
                                                     11 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                             + 
                                             
                                               
                                                 
                                                   s 
                                                   2 
                                                 
                                                 37 
                                               
                                               · 
                                               12 
                                               · 
                                               
                                                 ( 
                                                 
                                                   
                                                     2 
                                                      
                                                     k 
                                                   
                                                   + 
                                                   13 
                                                 
                                                 ) 
                                               
                                             
                                           
                                           } 
                                         
                                       
                                       ] 
                                     
                                   
                                 
                                 ] 
                               
                               + 
                             
                           
                         
                       
                       
                         
                           
                               
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                     π 
                                     37 
                                   
                                    
                                   
                                     
                                       s 
                                       3 
                                     
                                     · 
                                     23 
                                     · 
                                     24 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
         [0078]    And, when the 1 RB length sequence overlapped in the last 12 subcarrier region of the 3 RB length sequence, the cross correlation value can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       c 
                        
                       
                         ( 
                         
                           
                             d 
                             ; 
                             
                               s 
                               1 
                             
                           
                           , 
                           
                             s 
                             3 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           
                             g 
                             
                               1 
                                
                               RB 
                             
                           
                            
                           
                             ( 
                             
                               k 
                               ; 
                               
                                 s 
                                 1 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                             g 
                             
                               3 
                                
                               RB 
                             
                             * 
                           
                            
                           
                             ( 
                             
                               
                                 k 
                                 + 
                                 24 
                                 + 
                                 d 
                               
                               ; 
                               
                                 s 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         For 
                          
                         
                             
                         
                          
                         d 
                       
                       = 
                       0 
                     
                     , 
                     
                       
 
                     
                      
                     
                       
                         
                           
                             
                               c 
                                
                               
                                 ( 
                                 
                                   
                                     0 
                                     ; 
                                     
                                       s 
                                       1 
                                     
                                   
                                   , 
                                   
                                     s 
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             = 
                               
                              
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 exp 
                                  
                                 
                                   ( 
                                   
                                     
                                       - 
                                       j 
                                     
                                      
                                     
                                       π 
                                       
                                         N 
                                         1 
                                       
                                     
                                      
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       mod 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           , 
                                           
                                             N 
                                             - 
                                             1 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           mod 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               , 
                                               
                                                 N 
                                                 - 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                     π 
                                     
                                       N 
                                       3 
                                     
                                   
                                    
                                   
                                     
                                       s 
                                       3 
                                     
                                      
                                     
                                       ( 
                                       
                                         k 
                                         + 
                                         24 
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       k 
                                       + 
                                       25 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                               
                              
                             
                               
                                 [ 
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       0 
                                     
                                     10 
                                   
                                    
                                   
                                     exp 
                                      
                                     
                                       [ 
                                       
                                         jπ 
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       k 
                                                        
                                                       
                                                         ( 
                                                         
                                                           k 
                                                           + 
                                                           1 
                                                         
                                                         ) 
                                                       
                                                     
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           
                                                             s 
                                                             3 
                                                           
                                                           37 
                                                         
                                                         - 
                                                         
                                                           
                                                             s 
                                                             1 
                                                           
                                                           11 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                   + 
                                                 
                                               
                                             
                                             
                                               
                                                 
                                                   
                                                     
                                                       s 
                                                       2 
                                                     
                                                     37 
                                                   
                                                   · 
                                                   24 
                                                   · 
                                                   
                                                     ( 
                                                     
                                                       
                                                         2 
                                                          
                                                         k 
                                                       
                                                       + 
                                                       25 
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                             
                                           
                                           } 
                                         
                                       
                                       ] 
                                     
                                   
                                 
                                 ] 
                               
                               + 
                             
                           
                         
                       
                       
                         
                           
                               
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   j 
                                    
                                   
                                     π 
                                     37 
                                   
                                    
                                   
                                     
                                       s 
                                       3 
                                     
                                     · 
                                     35 
                                     · 
                                     36 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
         [0079]    According to the equations 11 and 12, it can also concluded that if the combination of sequence indexes (s 1  and s 3 ) meet the condition that the term of 
         [0000]    
       
         
           
             ( 
             
               
                 
                   s 
                   3 
                 
                 37 
               
               - 
               
                 
                   s 
                   1 
                 
                 11 
               
             
             ) 
           
         
       
     
         [0000]    becomes close to zero, the sequences indicated by these sequence indexes result in high cross correlation. So, if 1 RB length sequence and 3 RB length sequence are considered, the position where the overlapping is occurred is not change the grouping condition. 
         [0080]    According to the above examples, the present embodiment proposes to perform grouping sequences such that two sequence indexes among all the sequence indexes grouped into the same group meet the condition that the term (s 2 /N 2 −s 1 /N 1 ) becomes close to zero, when the two sequences having the length of N 1  and N 2  are considered. Here, N 1  and N 2  can be maximum relative prime numbers which are less than the resultant reference signal sequence. And, s 1  and s 2  mean the root indexes of the ZC sequences, and can be selected among the ranges of 1˜(N 1 −1) and 1˜(N 2 −1) respectively. 
         [0081]    Based on this concept, let&#39;s consider more general grouping method considering various length sequences. 
         [0082]      FIGS. 3 to 5  show conceptual diagrams of grouping sequences according to one embodiment of this invention. 
         [0083]    According to this embodiment, among various length sequences such as 1 RB, 2 RB, 3 RB . . . as shown in the  FIG. 3 , the sequences whose indexes meet the high cross correlation condition as stated above may be grouped into the same group. And, each of the sequence groups can be allocated to the same cell or node B. 
         [0084]    Generally, FDM is done with the unit of cell or Node B, so the inference caused by using the sequences having difference length can be minimized within one cell or Node B. So, by allocating the sequences having the high cross correlation relation to the same cell or Node B, the inter cell interference caused by using the different length sequences can be minimized. 
         [0085]    And, another embodiment of this invention proposes to perform grouping such that each of the groups contains at least one sequence of each length. By doing so, if the sequence group is allocated to the same cell or Node B, UE(s) located in that cell or Node B can be supported to use various length reference signal sequence. But specific grouping method can be variously defined. 
         [0086]    First, the number of sequences allocated to one group can be proportional to the number of RBs which corresponds to the reference signal sequence length. In  FIG. 3 , one sequence for 1 RB length sequence, two sequences for 2 RB length sequence, 3 sequences for 3 RB length sequence, and so on, are grouped. 
         [0087]    Second, the number of sequences allocated to one group can be a constant number. In  FIG. 4 , one sequence for each RB length sequence is grouped to the same group. 
         [0088]    And, the present embodiment can be defined to perform grouping such that the number of sequences allocated to one group is neither proportional to the sequence length nor remain constant.  FIG. 5  shows an example of grouping sequence such that one sequence for 1 RB length sequence, 2 sequences for 2 RB length sequence, 2 sequences for 3 RB length sequence, and 3 sequences for 4 RB length sequence, and so on, are grouped into one group. 
         [0089]    As like the above, if each group contains at least one sequence of each RB length, the maximum number of sequence per group can be defined. When the maximum number of sequence per group is defined, a method for selecting root index of the ZC sequence within the sequence number limit can be defined as follows. 
         [0090]    If one sequence is selected per each RB length sequence, and if one specific sequence with the index of s 1  and the length of N 1  is already selected for that group, one sequence per (having index of s 2 ) each RB length can be selected, of which index make the term of (s 2 /N 2 −s 1 /N 1 ) to be closest to zero, where N 2  is the sequence length corresponding to the considered RB length. And, if 2 sequences are selected per certain RB length sequence, and if one specific sequence with the index of s 1  and the length of N 1  is already selected for that group, two sequences per that RB length can be selected to make the term of (s 2 /N 2 −s 1 /N 1 ) to be close to zero. This can be more generalized to the maximum sequence number of “x” per each RB length. 
         [0091]    And, another grouping method can be defined as follows. If one sequence is selected per each RB length sequence, and if one specific sequence with the index of s 1  and the length of N 1  is already selected for that group, first, select certain number (y) of sequences among sequences which make the term (s 2 /N 2 −s 1 /N 1 ) to be close to certain value, and then, select one sequence among the y sequences which has high cross correlation relation with the sequence having the index of s 1 . And, if 2 sequences are selected per certain RB length sequence, and if one specific sequence with the index of s 1  and the length of N 1  is already selected for that group, first, select certain number (y) of sequences among sequences which make the term (s 2 /N 2 −s 1 /N 1 ) to be close to certain value, and then, select two sequences among the y sequences which have high cross correlation relation with the sequence having the index of s 1 . This can be more generalized to the maximum sequence number of “x” per each RB length. 
         [0092]    In the above examples, one specific sequence with the index of s 1  and the length of N 1  is firstly selected and becomes the reference for selecting rest of the sequence. This reference sequence can be defined to be 1 RB length sequence, 2 RB length sequence, 3 RB length sequence, and so on. But In the following explanation, let us presume that the reference sequence is the 3 RB length sequence. And, because the number of sequence indexes per 3 RB length is 30, the number of groups for grouping sequence according to this embodiment of the invention can be 30. 
         [0093]    Considering that the number of root indexes for 3 RB length sequence is 30, the number of root index selected for certain group can be determined as follows. 
         [0000]      round(the number of root index for certain RB length sequence/30)  [Equation 13]
 
         [0094]    Here, “round (z)” is a function of rounding off to a nearest integer nearest to z. 
         [0095]    By the equation 13, for 3 RB and 4 RB lengths, 1 sequence can be selected. And, for 5 RB˜6 RB lengths, 2 sequence can be selected. Further, for the length greater than the 6 RB length, 3 or more sequence can be selected, respectively. And, according to one embodiment of this invention, sequence with the length less than 3 RB length can be differently defined, such as not using ZC sequence. By doing so, the number of sequences selected for 1 RB length and 2 RB length can be determined to 1. 
         [0096]    To summarize, according to this embodiment, the number of sequence per groups can be defined as follows. 
         [0000]      {1RB,2RB,3RB,4RB,5RB,6RB,8RB,9RB,10RB,12RB,15RB,16RB,18RB,20RB,24RB,25RB, . . . }={1,1,1,1,2,2,3,3,4,5,6,6,7,8,9,9, . . . }  [Equation 14]
 
         [0097]    Based on this, the following tables 1-5 show an example of sequence grouping such that each group contains the number of sequences according to the equation 14, and the sequences selected per each group satisfy the high cross correlation relation as stated above. 
         [0098]    [Table 1] 
         [0000]    
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Group- 
                   
                   
                   
                   
                   
                   
               
               
                 index 
                   
                   
                   
                   
                   
                   
               
               
                 based 
                   
                   
                   
                   
                   
                   
               
               
                 on 
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  1 
                 1 
                 2 
                 2 
                 1 
                 2 
                 3 
                 3 
                 2 
                 4 
                 3 
                 4 
                 2 
               
               
                  2 
                 2 
                 3 
                 4 
                 3 
                 5 
                 4 
                 6 
                 5 
                 7 
                 7 
                 6 
                 8 
               
               
                  3 
                 3 
                 5 
                 6 
                 5 
                 7 
                 6 
                 9 
                 8 
                   
                 10 
                 11 
                 9 
               
               
                  4 
                 4 
                 6 
                 8 
                 7 
                 9 
                 10 
                 11 
                 12 
                   
                 14 
                 13 
                 15 
               
               
                  5 
                 5 
                 8 
                 10 
                 9 
                 11 
                 12 
                 14 
                 15 
                 13 
                 17 
                 18 
                 16 
               
               
                  6 
                 6 
                 9 
                 11 
                 12 
                 14 
                 13 
                 17 
                 18 
                 16 
                 21 
                 20 
                 22 
               
               
                  7 
                 7 
                 11 
                 13 
                 14 
                 16 
                 17 
                 20 
                 21 
                 19 
                 24 
                 25 
                 23 
               
               
                  8 
                 8 
                 12 
                 15 
                 16 
                 18 
                 19 
                 23 
                 22 
                 24 
                 28 
                 27 
                 29 
               
               
                  9 
                 9 
                 14 
                 17 
                 18 
                 21 
                 20 
                 26 
                 25 
                 27 
                 31 
                 32 
                 30 
               
               
                 10 
                 10 
                 15 
                 19 
                   
                 23 
                 22 
                 29 
                 28 
                 30 
                 35 
                 34 
                 36 
               
               
                 11 
                 11 
                 17 
                 21 
                   
                 25 
                 26 
                 32 
                 31 
                   
                 38 
                 37 
                 39 
               
               
                 12 
                 12 
                 18 
                 23 
                 22 
                 27 
                 28 
                 34 
                 35 
                   
                 41 
                 42 
                 40 
               
               
                 13 
                 13 
                 20 
                 25 
                 24 
                 30 
                 29 
                 37 
                 38 
                 36 
                 45 
                 44 
                 46 
               
               
                 14 
                 14 
                 21 
                 27 
                 26 
                 32 
                 33 
                 40 
                 41 
                 39 
                 48 
                 49 
                 47 
               
               
                 15 
                 15 
                 23 
                 29 
                 28 
                 34 
                 35 
                 43 
                 44 
                 42 
                 52 
                 51 
                 53 
               
               
                 16 
                 16 
                 24 
                 30 
                 31 
                 37 
                 36 
                 46 
                 45 
                 47 
                 55 
                 56 
                 54 
               
               
                 17 
                 17 
                 26 
                 32 
                 33 
                 39 
                 38 
                 49 
                 48 
                 50 
                 59 
                 58 
                 60 
               
               
                 18 
                 18 
                 27 
                 34 
                 35 
                 41 
                 42 
                 52 
                 51 
                 53 
                 62 
                 63 
                 61 
               
               
                 19 
                 19 
                 29 
                 36 
                 37 
                 44 
                 43 
                 55 
                 54 
                   
                 66 
                 65 
                 67 
               
               
                 20 
                 20 
                 30 
                 38 
                   
                 46 
                 45 
                 57 
                 58 
                   
                 69 
                 70 
                 68 
               
               
                 21 
                 21 
                 32 
                 40 
                   
                 48 
                 49 
                 60 
                 61 
                 59 
                 72 
                 73 
                 71 
               
               
                 22 
                 22 
                 33 
                 42 
                 41 
                 50 
                 51 
                 63 
                 64 
                 62 
                 76 
                 75 
                 77 
               
               
                 23 
                 23 
                 35 
                 44 
                 43 
                 53 
                 52 
                 66 
                 67 
                 65 
                 79 
                 80 
                 78 
               
               
                 24 
                 24 
                 36 
                 46 
                 45 
                 55 
                 54 
                 69 
                 68 
                 70 
                 83 
                 82 
                 84 
               
               
                 25 
                 25 
                 38 
                 48 
                 47 
                 57 
                 58 
                 72 
                 71 
                 73 
                 86 
                 87 
                 85 
               
               
                 26 
                 26 
                 39 
                 49 
                 50 
                 60 
                 59 
                 75 
                 74 
                 76 
                 90 
                 89 
                 91 
               
               
                 27 
                 27 
                 41 
                 51 
                 52 
                 62 
                 61 
                 78 
                 77 
                   
                 93 
                 94 
                 92 
               
               
                 28 
                 28 
                 42 
                 53 
                 54 
                 64 
                 65 
                 80 
                 81 
                   
                 97 
                 96 
                 98 
               
               
                 29 
                 29 
                 44 
                 55 
                 56 
                 66 
                 67 
                 83 
                 84 
                 82 
                 100 
                 101 
                 99 
               
               
                 30 
                 30 
                 45 
                 57 
                 58 
                 69 
                 68 
                 86 
                 87 
                 85 
                 104 
                 103 
                 105 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Group index 
                   
                   
                   
               
               
                 based on 3RBs 
                 10RB 
                 12RB 
                 15RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 4 
                 3 
                 5 
                 2 
                 4 
                 5 
                 3 
                 6 
                 2 
                 6 
                 5 
                 7 
                 4 
                 8 
                 3 
               
               
                 2 
                 7 
                 8 
                 6 
                   
                 9 
                 8 
                 10 
                 7 
                   
                 12 
                 11 
                 13 
                 10 
                 14 
                 9 
               
               
                 3 
                 11 
                 10 
                 12 
                   
                 13 
                 14 
                 12 
                 15 
                   
                 17 
                 18 
                 16 
                 19 
                 15 
                 20 
               
               
                 4 
                 15 
                 14 
                 16 
                 13 
                 18 
                 17 
                 19 
                 16 
                   
                 23 
                 24 
                 22 
                 25 
                 21 
               
               
                 5 
                 18 
                 19 
                 17 
                   
                 22 
                 23 
                 21 
                 24 
                   
                 29 
                 28 
                 30 
                 27 
                 31 
               
               
                 6 
                 22 
                 21 
                 23 
                   
                 27 
                 26 
                 28 
                 25 
                   
                 35 
                 34 
                 36 
                 33 
                 37 
                 32 
               
               
                 7 
                 26 
                 25 
                 27 
                 24 
                 31 
                 32 
                 30 
                 33 
                   
                 40 
                 41 
                 39 
                 42 
                 38 
                 43 
               
               
                 8 
                 29 
                 30 
                 28 
                   
                 36 
                 35 
                 37 
                 34 
                   
                 46 
                 47 
                 45 
                 48 
                 44 
               
               
                 9 
                 33 
                 32 
                 34 
                   
                 40 
                 41 
                 39 
                 42 
                   
                 52 
                 51 
                 53 
                 50 
                 54 
               
               
                 10 
                 36 
                 37 
                 35 
                 38 
                 45 
                 44 
                 46 
                 43 
                   
                 58 
                 57 
                 59 
                 56 
                 60 
                 55 
               
               
                 11 
                 40 
                 41 
                 39 
                   
                 49 
                 50 
                 48 
                 51 
                   
                 64 
                 63 
                 65 
                 62 
                 66 
                 61 
               
               
                 12 
                 44 
                 43 
                 45 
                   
                 54 
                 53 
                 55 
                 52 
                   
                 69 
                 70 
                 68 
                 71 
                 67 
                 72 
               
               
                 13 
                 47 
                 48 
                 46 
                 49 
                 58 
                 59 
                 57 
                 60 
                   
                 75 
                 76 
                 74 
                 77 
                 73 
               
               
                 14 
                 51 
                 52 
                 50 
                   
                 63 
                 62 
                 64 
                 61 
                   
                 81 
                 80 
                 82 
                 79 
                 83 
               
               
                 15 
                 55 
                 54 
                 56 
                   
                 67 
                 68 
                 66 
                 69 
                   
                 87 
                 86 
                 88 
                 85 
                 89 
                 84 
               
               
                 16 
                 58 
                 59 
                 57 
                   
                 72 
                 71 
                 73 
                 70 
                   
                 92 
                 93 
                 91 
                 94 
                 90 
                 95 
               
               
                 17 
                 62 
                 61 
                 63 
                   
                 76 
                 77 
                 75 
                 78 
                   
                 98 
                 99 
                 97 
                 100 
                 96 
               
               
                 18 
                 66 
                 65 
                 67 
                 64 
                 81 
                 80 
                 82 
                 79 
                   
                 104 
                 103 
                 105 
                 102 
                 106 
               
               
                 19 
                 69 
                 70 
                 68 
                   
                 85 
                 86 
                 84 
                 87 
                   
                 110 
                 109 
                 111 
                 108 
                 112 
                 107 
               
               
                 20 
                 73 
                 72 
                 74 
                   
                 90 
                 89 
                 91 
                 88 
                   
                 115 
                 116 
                 114 
                 117 
                 113 
                 118 
               
               
                 21 
                 77 
                 76 
                 78 
                 75 
                 94 
                 95 
                 93 
                 96 
                   
                 121 
                 122 
                 120 
                 123 
                 119 
                 124 
               
               
                 22 
                 80 
                 81 
                 79 
                   
                 99 
                 98 
                 100 
                 97 
                   
                 127 
                 128 
                 126 
                 129 
                 125 
               
               
                 23 
                 84 
                 83 
                 85 
                   
                 103 
                 104 
                 102 
                 105 
                   
                 133 
                 132 
                 134 
                 131 
                 135 
               
               
                 24 
                 87 
                 88 
                 86 
                 89 
                 108 
                 107 
                 109 
                 106 
                   
                 139 
                 138 
                 140 
                 137 
                 141 
                 136 
               
               
                 25 
                 91 
                 92 
                 90 
                   
                 112 
                 113 
                 111 
                 114 
                   
                 144 
                 145 
                 143 
                 146 
                 142 
                 147 
               
               
                 26 
                 95 
                 94 
                 96 
                   
                 117 
                 116 
                 118 
                 115 
                   
                 150 
                 151 
                 149 
                 152 
                 148 
               
               
                 27 
                 98 
                 99 
                 97 
                 100 
                 121 
                 122 
                 120 
                 123 
                   
                 156 
                 155 
                 157 
                 154 
                 158 
               
               
                 28 
                 102 
                 103 
                 101 
                   
                 126 
                 125 
                 127 
                 124 
                   
                 162 
                 161 
                 163 
                 160 
                 164 
                 159 
               
               
                 29 
                 106 
                 105 
                 107 
                   
                 130 
                 131 
                 129 
                 132 
                   
                 167 
                 168 
                 166 
                 169 
                 165 
                 170 
               
               
                 30 
                 109 
                 110 
                 108 
                 111 
                 135 
                 134 
                 136 
                 133 
                 137 
                 173 
                 174 
                 172 
                 175 
                 171 
                 176 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 Group index 
                   
                   
               
               
                 based on 3RBs 
                 16RB 
                 18RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 6 
                 7 
                 5 
                 8 
                 4 
                 9 
                 7 
                 6 
                 8 
                 5 
                 9 
                 4 
                 10 
               
               
                 2 
                 12 
                 13 
                 11 
                 14 
                 10 
                 15 
                 14 
                 13 
                 15 
                 12 
                 16 
                 11 
                 17 
               
               
                 3 
                 18 
                 19 
                 17 
                 20 
                 16 
                 21 
                 20 
                 21 
                 19 
                 22 
                 18 
                 23 
                 17 
               
               
                 4 
                 25 
                 24 
                 26 
                 23 
                 27 
                 22 
                 27 
                 28 
                 26 
                 29 
                 25 
                 30 
                 24 
               
               
                 5 
                 31 
                 30 
                 32 
                 29 
                 33 
                 28 
                 34 
                 35 
                 33 
                 36 
                 32 
                 37 
                 31 
               
               
                 6 
                 37 
                 36 
                 38 
                 35 
                 39 
                 34 
                 41 
                 40 
                 42 
                 39 
                 43 
                 38 
                 44 
               
               
                 7 
                 43 
                 44 
                 42 
                 45 
                 41 
                 46 
                 48 
                 47 
                 49 
                 46 
                 50 
                 45 
                 51 
               
               
                 8 
                 49 
                 50 
                 48 
                 51 
                 47 
                 52 
                 54 
                 55 
                 53 
                 56 
                 52 
                 57 
                 51 
               
               
                 9 
                 55 
                 56 
                 54 
                 57 
                 53 
                 58 
                 61 
                 62 
                 60 
                 63 
                 59 
                 64 
                 58 
               
               
                 10 
                 62 
                 61 
                 63 
                 60 
                 64 
                 59 
                 68 
                 69 
                 67 
                 70 
                 66 
                 71 
                 65 
               
               
                 11 
                 68 
                 67 
                 69 
                 66 
                 70 
                 65 
                 75 
                 74 
                 76 
                 73 
                 77 
                 72 
                 78 
               
               
                 12 
                 74 
                 73 
                 75 
                 72 
                 76 
                 71 
                 82 
                 81 
                 83 
                 80 
                 84 
                 79 
                 85 
               
               
                 13 
                 80 
                 81 
                 79 
                 82 
                 78 
                 83 
                 88 
                 89 
                 87 
                 90 
                 86 
                 91 
                 85 
               
               
                 14 
                 86 
                 87 
                 85 
                 88 
                 84 
                 89 
                 95 
                 96 
                 94 
                 97 
                 93 
                 98 
                 92 
               
               
                 15 
                 92 
                 93 
                 91 
                 94 
                 90 
                 95 
                 102 
                 103 
                 101 
                 104 
                 100 
                 105 
                 99 
               
               
                 16 
                 99 
                 98 
                 100 
                 97 
                 101 
                 96 
                 109 
                 108 
                 110 
                 107 
                 111 
                 106 
                 112 
               
               
                 17 
                 105 
                 104 
                 106 
                 103 
                 107 
                 102 
                 116 
                 115 
                 117 
                 114 
                 118 
                 113 
                 119 
               
               
                 18 
                 111 
                 110 
                 112 
                 109 
                 113 
                 108 
                 123 
                 122 
                 124 
                 121 
                 125 
                 120 
                 126 
               
               
                 19 
                 117 
                 118 
                 116 
                 119 
                 115 
                 120 
                 129 
                 130 
                 128 
                 131 
                 127 
                 132 
                 126 
               
               
                 20 
                 123 
                 124 
                 122 
                 125 
                 121 
                 126 
                 136 
                 137 
                 135 
                 138 
                 134 
                 139 
                 133 
               
               
                 21 
                 129 
                 130 
                 128 
                 131 
                 127 
                 132 
                 143 
                 142 
                 144 
                 141 
                 145 
                 140 
                 146 
               
               
                 22 
                 136 
                 135 
                 137 
                 134 
                 138 
                 133 
                 150 
                 149 
                 151 
                 148 
                 152 
                 147 
                 153 
               
               
                 23 
                 142 
                 141 
                 143 
                 140 
                 144 
                 139 
                 157 
                 156 
                 158 
                 155 
                 159 
                 154 
                 160 
               
               
                 24 
                 148 
                 147 
                 149 
                 146 
                 150 
                 145 
                 163 
                 164 
                 162 
                 165 
                 161 
                 166 
                 160 
               
               
                 25 
                 154 
                 155 
                 153 
                 156 
                 152 
                 157 
                 170 
                 171 
                 169 
                 172 
                 168 
                 173 
                 167 
               
               
                 26 
                 160 
                 161 
                 159 
                 162 
                 158 
                 163 
                 177 
                 176 
                 178 
                 175 
                 179 
                 174 
                 180 
               
               
                 27 
                 166 
                 167 
                 165 
                 168 
                 164 
                 169 
                 184 
                 183 
                 185 
                 182 
                 186 
                 181 
                 187 
               
               
                 28 
                 173 
                 172 
                 174 
                 171 
                 175 
                 170 
                 191 
                 190 
                 192 
                 189 
                 193 
                 188 
                 194 
               
               
                 29 
                 179 
                 178 
                 180 
                 177 
                 181 
                 176 
                 197 
                 198 
                 196 
                 199 
                 195 
                 200 
                 194 
               
               
                 30 
                 185 
                 184 
                 186 
                 183 
                 187 
                 182 
                 204 
                 205 
                 203 
                 206 
                 202 
                 207 
                 201 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Group index 
                   
                   
               
               
                 based on 3RBs 
                 20RB 
                 24RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 8 
                 7 
                 9 
                 6 
                 10 
                 5 
                 11 
                 4 
                 9 
                 10 
                 8 
                 11 
                 7 
                 12 
                 6 
                 13 
                 5 
               
               
                 2 
                 15 
                 16 
                 14 
                 17 
                 13 
                 18 
                 12 
                 19 
                 18 
                 19 
                 17 
                 20 
                 16 
                 21 
                 15 
                 22 
                 14 
               
               
                 3 
                 23 
                 24 
                 22 
                 25 
                 21 
                 26 
                 20 
                   
                 27 
                 28 
                 26 
                 29 
                 25 
                 30 
                 24 
                 31 
                 23 
               
               
                 4 
                 31 
                 30 
                 32 
                 29 
                 33 
                 28 
                 34 
                   
                 37 
                 36 
                 38 
                 35 
                 39 
                 34 
                 40 
                 33 
                 41 
               
               
                 5 
                 39 
                 38 
                 40 
                 37 
                 41 
                 36 
                 42 
                 35 
                 46 
                 45 
                 47 
                 44 
                 48 
                 43 
                 49 
                 42 
                 50 
               
               
                 6 
                 46 
                 47 
                 45 
                 48 
                 44 
                 49 
                 43 
                   
                 55 
                 54 
                 56 
                 53 
                 57 
                 52 
                 58 
                 51 
                 59 
               
               
                 7 
                 54 
                 53 
                 55 
                 52 
                 56 
                 51 
                 57 
                   
                 64 
                 63 
                 65 
                 62 
                 66 
                 61 
                 67 
                 60 
                 68 
               
               
                 8 
                 62 
                 61 
                 63 
                 60 
                 64 
                 59 
                 65 
                 58 
                 73 
                 74 
                 72 
                 75 
                 71 
                 76 
                 70 
                 77 
                 69 
               
               
                 9 
                 69 
                 70 
                 68 
                 71 
                 67 
                 72 
                 66 
                 73 
                 82 
                 83 
                 81 
                 84 
                 80 
                 85 
                 79 
                 86 
                 78 
               
               
                 10 
                 77 
                 78 
                 76 
                 79 
                 75 
                 80 
                 74 
                   
                 91 
                 92 
                 90 
                 93 
                 89 
                 94 
                 88 
                 95 
                 87 
               
               
                 11 
                 85 
                 84 
                 86 
                 83 
                 87 
                 82 
                 88 
                   
                 100 
                 101 
                 99 
                 102 
                 98 
                 103 
                 97 
                 104 
                 96 
               
               
                 12 
                 93 
                 92 
                 94 
                 91 
                 95 
                 90 
                 96 
                 89 
                 110 
                 109 
                 111 
                 108 
                 112 
                 107 
                 113 
                 106 
                 114 
               
               
                 13 
                 100 
                 101 
                 99 
                 102 
                 98 
                 103 
                 97 
                   
                 119 
                 118 
                 120 
                 117 
                 121 
                 116 
                 122 
                 115 
                 123 
               
               
                 14 
                 108 
                 107 
                 109 
                 106 
                 110 
                 105 
                 111 
                   
                 128 
                 127 
                 129 
                 126 
                 130 
                 125 
                 131 
                 124 
                 132 
               
               
                 15 
                 116 
                 115 
                 117 
                 114 
                 118 
                 113 
                 119 
                 112 
                 137 
                 136 
                 138 
                 135 
                 139 
                 134 
                 140 
                 133 
                 141 
               
               
                 16 
                 123 
                 124 
                 122 
                 125 
                 121 
                 126 
                 120 
                 127 
                 146 
                 147 
                 145 
                 148 
                 144 
                 149 
                 143 
                 150 
                 142 
               
               
                 17 
                 131 
                 132 
                 130 
                 133 
                 129 
                 134 
                 128 
                   
                 155 
                 156 
                 154 
                 157 
                 153 
                 158 
                 152 
                 159 
                 151 
               
               
                 18 
                 139 
                 138 
                 140 
                 137 
                 141 
                 136 
                 142 
                   
                 164 
                 165 
                 163 
                 166 
                 162 
                 167 
                 161 
                 168 
                 160 
               
               
                 19 
                 146 
                 147 
                 145 
                 148 
                 144 
                 149 
                 143 
                 150 
                 173 
                 174 
                 172 
                 175 
                 171 
                 178 
                 170 
                 177 
                 169 
               
               
                 20 
                 154 
                 155 
                 153 
                 156 
                 152 
                 157 
                 151 
                   
                 183 
                 182 
                 184 
                 181 
                 185 
                 180 
                 186 
                 179 
                 187 
               
               
                 21 
                 162 
                 161 
                 163 
                 160 
                 164 
                 159 
                 165 
                   
                 192 
                 191 
                 193 
                 190 
                 194 
                 189 
                 195 
                 188 
                 196 
               
               
                 22 
                 170 
                 169 
                 171 
                 168 
                 172 
                 167 
                 173 
                 166 
                 201 
                 200 
                 202 
                 199 
                 203 
                 198 
                 204 
                 197 
                 205 
               
               
                 23 
                 177 
                 178 
                 176 
                 179 
                 175 
                 180 
                 174 
                 181 
                 210 
                 209 
                 211 
                 208 
                 212 
                 207 
                 213 
                 206 
                 214 
               
               
                 24 
                 185 
                 186 
                 184 
                 187 
                 183 
                 188 
                 182 
                   
                 219 
                 220 
                 218 
                 221 
                 217 
                 222 
                 216 
                 223 
                 215 
               
               
                 25 
                 193 
                 192 
                 194 
                 191 
                 195 
                 190 
                 196 
                   
                 228 
                 229 
                 227 
                 230 
                 226 
                 231 
                 225 
                 232 
                 224 
               
               
                 26 
                 200 
                 201 
                 199 
                 202 
                 198 
                 203 
                 197 
                 204 
                 237 
                 238 
                 236 
                 239 
                 235 
                 240 
                 234 
                 241 
                 233 
               
               
                 27 
                 208 
                 209 
                 207 
                 210 
                 206 
                 211 
                 205 
                   
                 246 
                 247 
                 245 
                 248 
                 244 
                 249 
                 243 
                 250 
                 242 
               
               
                 28 
                 216 
                 215 
                 217 
                 214 
                 218 
                 213 
                 219 
                   
                 256 
                 255 
                 257 
                 254 
                 258 
                 253 
                 259 
                 252 
                 260 
               
               
                 29 
                 224 
                 223 
                 225 
                 222 
                 226 
                 221 
                 227 
                 220 
                 265 
                 264 
                 266 
                 263 
                 267 
                 262 
                 268 
                 261 
                 269 
               
               
                 30 
                 231 
                 232 
                 230 
                 233 
                 229 
                 234 
                 228 
                 235 
                 274 
                 273 
                 275 
                 272 
                 276 
                 271 
                 277 
                 270 
                 278 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 Group 
                   
               
               
                 index 
                   
               
               
                 based 
                   
               
               
                 on 
                   
               
               
                 3RBs 
                 25RBs 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 9 
                 10 
                 8 
                 11 
                 7 
                 12 
                 6 
                 13 
                 5 
               
               
                 2 
                 19 
                 18 
                 20 
                 17 
                 21 
                 16 
                 22 
                 15 
                 23 
               
               
                 3 
                 28 
                 29 
                 27 
                 30 
                 26 
                 31 
                 25 
                 32 
                 24 
               
               
                 4 
                 38 
                 37 
                 39 
                 36 
                 40 
                 35 
                 41 
                 34 
                 42 
               
               
                 5 
                 47 
                 48 
                 46 
                 49 
                 45 
                 50 
                 44 
                 51 
                 43 
               
               
                 6 
                 57 
                 56 
                 58 
                 55 
                 59 
                 54 
                 60 
                 53 
                 61 
               
               
                 7 
                 66 
                 67 
                 65 
                 68 
                 64 
                 69 
                 63 
                 70 
                 62 
               
               
                 8 
                 76 
                 75 
                 77 
                 74 
                 78 
                 73 
                 79 
                 72 
                 80 
               
               
                 9 
                 85 
                 86 
                 84 
                 87 
                 83 
                 88 
                 82 
                 89 
                 81 
               
               
                 10 
                 95 
                 94 
                 96 
                 93 
                 97 
                 92 
                 98 
                 91 
                 99 
               
               
                 11 
                 104 
                 103 
                 105 
                 102 
                 106 
                 101 
                 107 
                 100 
                 108 
               
               
                 12 
                 113 
                 114 
                 112 
                 115 
                 111 
                 116 
                 110 
                 117 
                 109 
               
               
                 13 
                 123 
                 122 
                 124 
                 121 
                 125 
                 120 
                 126 
                 119 
                 127 
               
               
                 14 
                 132 
                 133 
                 131 
                 134 
                 130 
                 135 
                 129 
                 136 
                 128 
               
               
                 15 
                 142 
                 141 
                 143 
                 140 
                 144 
                 139 
                 145 
                 138 
                 146 
               
               
                 16 
                 151 
                 152 
                 150 
                 153 
                 149 
                 154 
                 148 
                 155 
                 147 
               
               
                 17 
                 161 
                 160 
                 162 
                 159 
                 163 
                 158 
                 164 
                 157 
                 165 
               
               
                 18 
                 170 
                 171 
                 169 
                 172 
                 168 
                 173 
                 167 
                 174 
                 166 
               
               
                 19 
                 180 
                 179 
                 181 
                 178 
                 182 
                 177 
                 183 
                 176 
                 184 
               
               
                 20 
                 189 
                 190 
                 188 
                 191 
                 187 
                 192 
                 186 
                 193 
                 185 
               
               
                 21 
                 198 
                 199 
                 197 
                 200 
                 196 
                 201 
                 195 
                 202 
                 194 
               
               
                 22 
                 208 
                 207 
                 209 
                 206 
                 210 
                 205 
                 211 
                 204 
                 212 
               
               
                 23 
                 217 
                 218 
                 216 
                 219 
                 215 
                 220 
                 214 
                 221 
                 213 
               
               
                 24 
                 227 
                 226 
                 228 
                 225 
                 229 
                 224 
                 230 
                 223 
                 231 
               
               
                 25 
                 236 
                 237 
                 235 
                 238 
                 234 
                 239 
                 233 
                 240 
                 232 
               
               
                 26 
                 246 
                 245 
                 247 
                 244 
                 248 
                 243 
                 249 
                 242 
                 250 
               
               
                 27 
                 255 
                 256 
                 254 
                 257 
                 253 
                 258 
                 252 
                 259 
                 251 
               
               
                 28 
                 265 
                 264 
                 266 
                 263 
                 267 
                 262 
                 268 
                 261 
                 269 
               
               
                 29 
                 274 
                 275 
                 273 
                 276 
                 272 
                 277 
                 271 
                 278 
                 270 
               
               
                 30 
                 284 
                 283 
                 285 
                 282 
                 286 
                 281 
                 287 
                 280 
                 288 
               
               
                   
               
             
          
         
       
     
         [0099]    In the tables 1˜5, 1 RB and 2 RB length sequence are not shown because 1 RB and 2 RB length sequence are differently defined. 
         [0100]    And, in another example, considering that the number of root indexes for 3 RB length sequence is 30, the number of root index selected for certain group can be determined as follows. 
         [0000]      floor(the number of root index for certain RB length sequence/30)  [Equation 15]
 
         [0101]    Here, floor (z) is a function of making the greatest integer not greater than z. 
         [0102]    By the equation 15, for 3˜5 RB lengths, 1 sequence can be selected. And, for 6˜8 RB lengths, 2 sequence can be selected. Further, for the length greater than the 9 RB length, 3 or more sequence can be selected, respectively. And, according to one embodiment of this invention, sequence with the length less than 3 RB length can be differently defined, such as not using ZC sequence. By doing so, the number of sequences selected for 1 RB length and 2 RB length can be determined to 1. 
         [0103]    To summarize, according to this embodiment, the number of sequence per groups can be defined as follows. 
         [0000]      {1RB,2RB,3RB,4RB,5RB,6RB,8RB,9RB,10RB,12RB,15RB,16RB,18RB,20RB,24RB,25RB, . . . }={1,1,1,1,1,2,2,3,3,4,5,6,7,7,9,9, . . . }  [Equation 16]
 
         [0104]    Based on this, the following tables 6-8 show an example of sequence grouping such that each group contains the number of sequences according to the equation 16, and the sequences selected per each group satisfy the high cross correlation relation as stated above. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 2 
                 2 
                 3 
                 3 
                 2 
                 3 
                 4 
                 2 
                 4 
                 3 
                 5 
               
               
                 2 
                 2 
                 3 
                 4 
                 5 
                 4 
                 6 
                 5 
                 7 
                 6 
                 8 
                 7 
                 8 
                 6 
               
               
                 3 
                 3 
                 5 
                 6 
                 7 
                 6 
                 9 
                 8 
                 10 
                 11 
                 9 
                 11 
                 10 
                 12 
               
               
                 4 
                 4 
                 6 
                 8 
                 9 
                 10 
                 11 
                 12 
                 14 
                 13 
                 15 
                 15 
                 14 
                 16 
               
               
                 5 
                 5 
                 8 
                 10 
                 11 
                 12 
                 14 
                 15 
                 17 
                 18 
                 16 
                 18 
                 19 
                 17 
               
               
                 6 
                 6 
                 9 
                 11 
                 14 
                 13 
                 17 
                 18 
                 21 
                 20 
                 22 
                 22 
                 21 
                 23 
               
               
                 7 
                 7 
                 11 
                 13 
                 16 
                 17 
                 20 
                 21 
                 24 
                 25 
                 23 
                 26 
                 25 
                 27 
               
               
                 8 
                 8 
                 12 
                 15 
                 18 
                 19 
                 23 
                 22 
                 28 
                 27 
                 29 
                 29 
                 30 
                 28 
               
               
                 9 
                 9 
                 14 
                 17 
                 21 
                 20 
                 26 
                 25 
                 31 
                 32 
                 30 
                 33 
                 32 
                 34 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 22 
                 29 
                 28 
                 35 
                 34 
                 36 
                 36 
                 37 
                 35 
               
               
                 11 
                 11 
                 17 
                 21 
                 25 
                 26 
                 32 
                 31 
                 38 
                 37 
                 39 
                 40 
                 41 
                 39 
               
               
                 12 
                 12 
                 18 
                 23 
                 27 
                 28 
                 34 
                 35 
                 41 
                 42 
                 40 
                 44 
                 43 
                 45 
               
               
                 13 
                 13 
                 20 
                 25 
                 30 
                 29 
                 37 
                 38 
                 45 
                 44 
                 46 
                 47 
                 48 
                 46 
               
               
                 14 
                 14 
                 21 
                 27 
                 32 
                 33 
                 40 
                 41 
                 48 
                 49 
                 47 
                 51 
                 52 
                 50 
               
               
                 15 
                 15 
                 23 
                 29 
                 34 
                 35 
                 43 
                 44 
                 52 
                 51 
                 53 
                 55 
                 54 
                 56 
               
               
                 16 
                 16 
                 24 
                 30 
                 37 
                 36 
                 46 
                 45 
                 55 
                 56 
                 54 
                 58 
                 59 
                 57 
               
               
                 17 
                 17 
                 26 
                 32 
                 39 
                 38 
                 49 
                 48 
                 59 
                 58 
                 60 
                 62 
                 61 
                 63 
               
               
                 18 
                 18 
                 27 
                 34 
                 41 
                 42 
                 52 
                 51 
                 62 
                 63 
                 61 
                 66 
                 65 
                 67 
               
               
                 19 
                 19 
                 29 
                 36 
                 44 
                 43 
                 55 
                 54 
                 66 
                 65 
                 67 
                 69 
                 70 
                 68 
               
               
                 20 
                 20 
                 30 
                 38 
                 46 
                 45 
                 57 
                 58 
                 69 
                 70 
                 68 
                 73 
                 72 
                 74 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 49 
                 60 
                 61 
                 72 
                 73 
                 71 
                 77 
                 76 
                 78 
               
               
                 22 
                 22 
                 33 
                 42 
                 50 
                 51 
                 63 
                 64 
                 76 
                 75 
                 77 
                 80 
                 81 
                 79 
               
               
                 23 
                 23 
                 35 
                 44 
                 53 
                 52 
                 66 
                 67 
                 79 
                 80 
                 78 
                 84 
                 83 
                 85 
               
               
                 24 
                 24 
                 36 
                 46 
                 55 
                 54 
                 69 
                 68 
                 83 
                 82 
                 84 
                 87 
                 88 
                 86 
               
               
                 25 
                 25 
                 38 
                 48 
                 57 
                 58 
                 72 
                 71 
                 86 
                 87 
                 85 
                 91 
                 92 
                 90 
               
               
                 26 
                 26 
                 39 
                 49 
                 60 
                 59 
                 75 
                 74 
                 90 
                 89 
                 91 
                 95 
                 94 
                 96 
               
               
                 27 
                 27 
                 41 
                 51 
                 62 
                 61 
                 78 
                 77 
                 93 
                 94 
                 92 
                 98 
                 99 
                 97 
               
               
                 28 
                 28 
                 42 
                 53 
                 64 
                 65 
                 80 
                 81 
                 97 
                 96 
                 98 
                 102 
                 103 
                 101 
               
               
                 29 
                 29 
                 44 
                 55 
                 66 
                 67 
                 83 
                 84 
                 100 
                 101 
                 99 
                 106 
                 105 
                 107 
               
               
                 30 
                 30 
                 45 
                 57 
                 69 
                 68 
                 86 
                 87 
                 104 
                 103 
                 105 
                 109 
                 110 
                 108 
               
               
                   
               
             
          
           
               
                   
                 Gr. Idx 
                   
                   
               
               
                   
                 3RBs 
                 12RB 
                 15RB 
               
               
                   
               
             
          
           
               
                   
                 1 
                 4 
                 5 
                 3 
                 6 
                 6 
                 5 
                 7 
                 4 
                 8 
               
               
                   
                 2 
                 9 
                 8 
                 10 
                 7 
                 12 
                 11 
                 13 
                 10 
                 14 
               
               
                   
                 3 
                 13 
                 14 
                 12 
                 15 
                 17 
                 18 
                 16 
                 19 
                 15 
               
               
                   
                 4 
                 18 
                 17 
                 19 
                 16 
                 23 
                 24 
                 22 
                 25 
                 21 
               
               
                   
                 5 
                 22 
                 23 
                 21 
                 24 
                 29 
                 28 
                 30 
                 27 
                 31 
               
               
                   
                 6 
                 27 
                 26 
                 28 
                 25 
                 35 
                 34 
                 36 
                 33 
                 37 
               
               
                   
                 7 
                 31 
                 32 
                 30 
                 33 
                 40 
                 41 
                 39 
                 42 
                 38 
               
               
                   
                 8 
                 36 
                 35 
                 37 
                 34 
                 46 
                 47 
                 45 
                 48 
                 44 
               
               
                   
                 9 
                 40 
                 41 
                 39 
                 42 
                 52 
                 51 
                 53 
                 50 
                 54 
               
               
                   
                 10 
                 45 
                 44 
                 46 
                 43 
                 58 
                 57 
                 59 
                 56 
                 60 
               
               
                   
                 11 
                 49 
                 50 
                 48 
                 51 
                 64 
                 63 
                 65 
                 62 
                 66 
               
               
                   
                 12 
                 54 
                 53 
                 55 
                 52 
                 69 
                 70 
                 68 
                 71 
                 67 
               
               
                   
                 13 
                 58 
                 59 
                 57 
                 60 
                 75 
                 76 
                 74 
                 77 
                 73 
               
               
                   
                 14 
                 63 
                 62 
                 64 
                 61 
                 81 
                 80 
                 82 
                 79 
                 83 
               
               
                   
                 15 
                 67 
                 68 
                 66 
                 69 
                 87 
                 86 
                 88 
                 85 
                 89 
               
               
                   
                 16 
                 72 
                 71 
                 73 
                 70 
                 92 
                 93 
                 91 
                 94 
                 90 
               
               
                   
                 17 
                 76 
                 77 
                 75 
                 78 
                 98 
                 99 
                 97 
                 100 
                 96 
               
               
                   
                 18 
                 81 
                 80 
                 82 
                 79 
                 104 
                 103 
                 105 
                 102 
                 106 
               
               
                   
                 19 
                 85 
                 86 
                 84 
                 87 
                 110 
                 109 
                 111 
                 108 
                 112 
               
               
                   
                 20 
                 90 
                 89 
                 91 
                 88 
                 115 
                 116 
                 114 
                 117 
                 113 
               
               
                   
                 21 
                 94 
                 95 
                 93 
                 96 
                 121 
                 122 
                 120 
                 123 
                 119 
               
               
                   
                 22 
                 99 
                 98 
                 100 
                 97 
                 127 
                 128 
                 126 
                 129 
                 125 
               
               
                   
                 23 
                 103 
                 104 
                 102 
                 105 
                 133 
                 132 
                 134 
                 131 
                 135 
               
               
                   
                 24 
                 108 
                 107 
                 109 
                 106 
                 139 
                 138 
                 140 
                 137 
                 141 
               
               
                   
                 25 
                 112 
                 113 
                 111 
                 114 
                 144 
                 145 
                 143 
                 146 
                 142 
               
               
                   
                 26 
                 117 
                 116 
                 118 
                 115 
                 150 
                 151 
                 149 
                 152 
                 148 
               
               
                   
                 27 
                 121 
                 122 
                 120 
                 123 
                 156 
                 155 
                 157 
                 154 
                 158 
               
               
                   
                 28 
                 126 
                 125 
                 127 
                 124 
                 162 
                 161 
                 163 
                 160 
                 164 
               
               
                   
                 29 
                 130 
                 131 
                 129 
                 132 
                 167 
                 168 
                 166 
                 169 
                 165 
               
               
                   
                 30 
                 135 
                 134 
                 136 
                 133 
                 173 
                 174 
                 172 
                 175 
                 171 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 Gr. 
                   
                   
                   
               
               
                 Idx 
                   
                   
                   
               
               
                 3RBs 
                 16RB 
                 18RB 
                 20RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 6 
                 7 
                 5 
                 8 
                 4 
                 9 
                 7 
                 6 
                 8 
                 5 
                 9 
                 4 
                 10 
                 8 
                 7 
                 9 
                 6 
                 10 
                 5 
                 11 
               
               
                 2 
                 12 
                 13 
                 11 
                 14 
                 10 
                 15 
                 14 
                 13 
                 15 
                 12 
                 16 
                 11 
                 17 
                 15 
                 16 
                 14 
                 17 
                 13 
                 18 
                 12 
               
               
                 3 
                 18 
                 19 
                 17 
                 20 
                 16 
                 21 
                 20 
                 21 
                 19 
                 22 
                 18 
                 23 
                 17 
                 23 
                 24 
                 22 
                 25 
                 21 
                 26 
                 20 
               
               
                 4 
                 25 
                 24 
                 26 
                 23 
                 27 
                 22 
                 27 
                 28 
                 26 
                 29 
                 25 
                 30 
                 24 
                 31 
                 30 
                 32 
                 29 
                 33 
                 28 
                 34 
               
               
                 5 
                 31 
                 30 
                 32 
                 29 
                 33 
                 28 
                 34 
                 35 
                 33 
                 36 
                 32 
                 37 
                 31 
                 39 
                 38 
                 40 
                 37 
                 41 
                 36 
                 42 
               
               
                 6 
                 37 
                 36 
                 38 
                 35 
                 39 
                 34 
                 41 
                 40 
                 42 
                 39 
                 43 
                 38 
                 44 
                 46 
                 47 
                 45 
                 48 
                 44 
                 49 
                 43 
               
               
                 7 
                 43 
                 44 
                 42 
                 45 
                 41 
                 46 
                 48 
                 47 
                 49 
                 46 
                 50 
                 45 
                 51 
                 54 
                 53 
                 55 
                 52 
                 56 
                 51 
                 57 
               
               
                 8 
                 49 
                 50 
                 48 
                 51 
                 47 
                 52 
                 54 
                 55 
                 53 
                 56 
                 52 
                 57 
                 51 
                 62 
                 61 
                 63 
                 60 
                 64 
                 59 
                 65 
               
               
                 9 
                 55 
                 56 
                 54 
                 57 
                 53 
                 58 
                 61 
                 62 
                 60 
                 63 
                 59 
                 64 
                 58 
                 69 
                 70 
                 68 
                 71 
                 67 
                 72 
                 66 
               
               
                 10 
                 62 
                 61 
                 63 
                 60 
                 64 
                 59 
                 68 
                 69 
                 67 
                 70 
                 66 
                 71 
                 65 
                 77 
                 78 
                 76 
                 79 
                 75 
                 80 
                 74 
               
               
                 11 
                 68 
                 67 
                 69 
                 66 
                 70 
                 65 
                 75 
                 74 
                 76 
                 73 
                 77 
                 72 
                 78 
                 85 
                 84 
                 86 
                 83 
                 87 
                 82 
                 88 
               
               
                 12 
                 74 
                 73 
                 75 
                 72 
                 76 
                 71 
                 82 
                 81 
                 83 
                 80 
                 84 
                 79 
                 85 
                 93 
                 92 
                 94 
                 91 
                 95 
                 90 
                 96 
               
               
                 13 
                 80 
                 81 
                 79 
                 82 
                 78 
                 83 
                 88 
                 89 
                 87 
                 90 
                 86 
                 91 
                 85 
                 100 
                 101 
                 99 
                 102 
                 98 
                 103 
                 97 
               
               
                 14 
                 86 
                 87 
                 85 
                 88 
                 84 
                 89 
                 95 
                 96 
                 94 
                 97 
                 93 
                 98 
                 92 
                 108 
                 107 
                 109 
                 106 
                 110 
                 105 
                 111 
               
               
                 15 
                 92 
                 93 
                 91 
                 94 
                 90 
                 95 
                 102 
                 103 
                 101 
                 104 
                 100 
                 105 
                 99 
                 116 
                 115 
                 117 
                 114 
                 118 
                 113 
                 119 
               
               
                 16 
                 99 
                 98 
                 100 
                 97 
                 101 
                 96 
                 109 
                 108 
                 110 
                 107 
                 111 
                 106 
                 112 
                 123 
                 124 
                 122 
                 125 
                 121 
                 126 
                 120 
               
               
                 17 
                 105 
                 104 
                 106 
                 103 
                 107 
                 102 
                 116 
                 115 
                 117 
                 114 
                 118 
                 113 
                 119 
                 131 
                 132 
                 130 
                 133 
                 129 
                 134 
                 128 
               
               
                 18 
                 111 
                 110 
                 112 
                 109 
                 113 
                 108 
                 123 
                 122 
                 124 
                 121 
                 125 
                 120 
                 126 
                 139 
                 138 
                 140 
                 137 
                 141 
                 136 
                 142 
               
               
                 19 
                 117 
                 118 
                 116 
                 119 
                 115 
                 120 
                 129 
                 130 
                 128 
                 131 
                 127 
                 132 
                 126 
                 146 
                 147 
                 145 
                 148 
                 144 
                 149 
                 143 
               
               
                 20 
                 123 
                 124 
                 122 
                 125 
                 121 
                 126 
                 136 
                 137 
                 135 
                 138 
                 134 
                 139 
                 133 
                 154 
                 155 
                 153 
                 156 
                 152 
                 157 
                 151 
               
               
                 21 
                 129 
                 130 
                 128 
                 131 
                 127 
                 132 
                 143 
                 142 
                 144 
                 141 
                 145 
                 140 
                 146 
                 162 
                 161 
                 163 
                 160 
                 164 
                 159 
                 165 
               
               
                 22 
                 136 
                 135 
                 137 
                 134 
                 138 
                 133 
                 150 
                 149 
                 151 
                 148 
                 152 
                 147 
                 153 
                 170 
                 169 
                 171 
                 168 
                 172 
                 167 
                 173 
               
               
                 23 
                 142 
                 141 
                 143 
                 140 
                 144 
                 139 
                 157 
                 156 
                 158 
                 155 
                 159 
                 154 
                 160 
                 177 
                 178 
                 176 
                 179 
                 175 
                 180 
                 174 
               
               
                 24 
                 148 
                 147 
                 149 
                 146 
                 150 
                 145 
                 163 
                 164 
                 162 
                 165 
                 161 
                 166 
                 160 
                 185 
                 186 
                 184 
                 187 
                 183 
                 188 
                 182 
               
               
                 25 
                 154 
                 155 
                 153 
                 156 
                 152 
                 157 
                 170 
                 171 
                 169 
                 172 
                 168 
                 173 
                 167 
                 193 
                 192 
                 194 
                 191 
                 195 
                 190 
                 196 
               
               
                 26 
                 160 
                 161 
                 159 
                 162 
                 158 
                 163 
                 177 
                 176 
                 178 
                 175 
                 179 
                 174 
                 180 
                 200 
                 201 
                 199 
                 202 
                 198 
                 203 
                 197 
               
               
                 27 
                 166 
                 167 
                 165 
                 168 
                 164 
                 169 
                 184 
                 183 
                 185 
                 182 
                 186 
                 181 
                 187 
                 208 
                 209 
                 207 
                 210 
                 206 
                 211 
                 205 
               
               
                 28 
                 173 
                 172 
                 174 
                 171 
                 175 
                 170 
                 191 
                 190 
                 192 
                 189 
                 193 
                 188 
                 194 
                 216 
                 215 
                 217 
                 214 
                 218 
                 213 
                 219 
               
               
                 29 
                 179 
                 178 
                 180 
                 177 
                 181 
                 176 
                 197 
                 198 
                 196 
                 199 
                 195 
                 200 
                 194 
                 224 
                 223 
                 225 
                 222 
                 226 
                 221 
                 227 
               
               
                 30 
                 185 
                 184 
                 186 
                 183 
                 187 
                 182 
                 204 
                 205 
                 203 
                 206 
                 202 
                 207 
                 201 
                 231 
                 232 
                 230 
                 233 
                 229 
                 234 
                 228 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Gr. 
                   
                   
               
               
                 Idx 
                   
                   
               
               
                 3RBs 
                 24RB 
                 25RBs 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 9 
                 10 
                 8 
                 11 
                 7 
                 12 
                 6 
                 13 
                 5 
                 9 
                 10 
                 8 
                 11 
                 7 
                 12 
                 6 
                 13 
                 5 
               
               
                 2 
                 18 
                 19 
                 17 
                 20 
                 16 
                 21 
                 15 
                 22 
                 14 
                 19 
                 18 
                 20 
                 17 
                 21 
                 16 
                 22 
                 15 
                 23 
               
               
                 3 
                 27 
                 28 
                 26 
                 29 
                 25 
                 30 
                 24 
                 31 
                 23 
                 28 
                 29 
                 27 
                 30 
                 26 
                 31 
                 25 
                 32 
                 24 
               
               
                 4 
                 37 
                 36 
                 38 
                 35 
                 39 
                 34 
                 40 
                 33 
                 41 
                 38 
                 37 
                 39 
                 36 
                 40 
                 35 
                 41 
                 34 
                 42 
               
               
                 5 
                 46 
                 45 
                 47 
                 44 
                 48 
                 43 
                 49 
                 42 
                 50 
                 47 
                 48 
                 46 
                 49 
                 45 
                 50 
                 44 
                 51 
                 43 
               
               
                 6 
                 55 
                 54 
                 56 
                 53 
                 57 
                 52 
                 58 
                 51 
                 59 
                 57 
                 56 
                 58 
                 55 
                 59 
                 54 
                 60 
                 53 
                 61 
               
               
                 7 
                 64 
                 63 
                 65 
                 62 
                 66 
                 61 
                 67 
                 60 
                 68 
                 66 
                 67 
                 65 
                 68 
                 64 
                 69 
                 63 
                 70 
                 62 
               
               
                 8 
                 73 
                 74 
                 72 
                 75 
                 71 
                 76 
                 70 
                 77 
                 69 
                 76 
                 75 
                 77 
                 74 
                 78 
                 73 
                 79 
                 72 
                 80 
               
               
                 9 
                 82 
                 83 
                 81 
                 84 
                 80 
                 85 
                 79 
                 86 
                 78 
                 85 
                 86 
                 84 
                 87 
                 83 
                 88 
                 82 
                 89 
                 81 
               
               
                 10 
                 91 
                 92 
                 90 
                 93 
                 89 
                 94 
                 88 
                 95 
                 87 
                 95 
                 94 
                 96 
                 93 
                 97 
                 92 
                 98 
                 91 
                 99 
               
               
                 11 
                 100 
                 101 
                 99 
                 102 
                 98 
                 103 
                 97 
                 104 
                 96 
                 104 
                 103 
                 105 
                 102 
                 106 
                 101 
                 107 
                 100 
                 108 
               
               
                 12 
                 110 
                 109 
                 111 
                 108 
                 112 
                 107 
                 113 
                 106 
                 114 
                 113 
                 114 
                 112 
                 115 
                 111 
                 116 
                 110 
                 117 
                 109 
               
               
                 13 
                 119 
                 118 
                 120 
                 117 
                 121 
                 116 
                 122 
                 115 
                 123 
                 123 
                 122 
                 124 
                 121 
                 125 
                 120 
                 126 
                 119 
                 127 
               
               
                 14 
                 128 
                 127 
                 129 
                 126 
                 130 
                 125 
                 131 
                 124 
                 132 
                 132 
                 133 
                 131 
                 134 
                 130 
                 135 
                 129 
                 136 
                 128 
               
               
                 15 
                 137 
                 136 
                 138 
                 135 
                 139 
                 134 
                 140 
                 133 
                 141 
                 142 
                 141 
                 143 
                 140 
                 144 
                 139 
                 145 
                 138 
                 146 
               
               
                 16 
                 146 
                 147 
                 145 
                 148 
                 144 
                 149 
                 143 
                 150 
                 142 
                 151 
                 152 
                 150 
                 153 
                 149 
                 154 
                 148 
                 155 
                 147 
               
               
                 17 
                 155 
                 156 
                 154 
                 157 
                 153 
                 158 
                 152 
                 159 
                 151 
                 161 
                 160 
                 162 
                 159 
                 163 
                 158 
                 164 
                 157 
                 165 
               
               
                 18 
                 164 
                 165 
                 163 
                 166 
                 162 
                 167 
                 161 
                 168 
                 160 
                 170 
                 171 
                 169 
                 172 
                 168 
                 173 
                 167 
                 174 
                 166 
               
               
                 19 
                 173 
                 174 
                 172 
                 175 
                 171 
                 176 
                 170 
                 177 
                 169 
                 180 
                 179 
                 181 
                 178 
                 182 
                 177 
                 183 
                 176 
                 184 
               
               
                 20 
                 183 
                 182 
                 184 
                 181 
                 185 
                 180 
                 186 
                 179 
                 187 
                 189 
                 190 
                 188 
                 191 
                 187 
                 192 
                 186 
                 193 
                 185 
               
               
                 21 
                 192 
                 191 
                 193 
                 190 
                 194 
                 189 
                 195 
                 188 
                 196 
                 198 
                 199 
                 197 
                 200 
                 196 
                 201 
                 195 
                 202 
                 194 
               
               
                 22 
                 201 
                 200 
                 202 
                 199 
                 203 
                 198 
                 204 
                 197 
                 205 
                 208 
                 207 
                 209 
                 206 
                 210 
                 205 
                 211 
                 204 
                 212 
               
               
                 23 
                 210 
                 209 
                 211 
                 208 
                 212 
                 207 
                 213 
                 206 
                 214 
                 217 
                 218 
                 216 
                 219 
                 215 
                 220 
                 214 
                 221 
                 213 
               
               
                 24 
                 219 
                 220 
                 218 
                 221 
                 217 
                 222 
                 216 
                 223 
                 215 
                 227 
                 226 
                 228 
                 225 
                 229 
                 224 
                 230 
                 223 
                 231 
               
               
                 25 
                 228 
                 229 
                 227 
                 230 
                 226 
                 231 
                 225 
                 232 
                 224 
                 236 
                 237 
                 235 
                 238 
                 234 
                 239 
                 233 
                 240 
                 232 
               
               
                 26 
                 237 
                 238 
                 236 
                 239 
                 235 
                 240 
                 234 
                 241 
                 233 
                 246 
                 245 
                 247 
                 244 
                 248 
                 243 
                 249 
                 242 
                 250 
               
               
                 27 
                 246 
                 247 
                 245 
                 248 
                 244 
                 249 
                 243 
                 250 
                 242 
                 255 
                 256 
                 254 
                 257 
                 253 
                 258 
                 252 
                 259 
                 251 
               
               
                 28 
                 256 
                 255 
                 257 
                 254 
                 258 
                 253 
                 259 
                 252 
                 260 
                 265 
                 264 
                 266 
                 263 
                 267 
                 262 
                 268 
                 261 
                 269 
               
               
                 29 
                 265 
                 264 
                 266 
                 263 
                 267 
                 262 
                 268 
                 261 
                 269 
                 274 
                 275 
                 273 
                 276 
                 272 
                 277 
                 271 
                 278 
                 270 
               
               
                 30 
                 274 
                 273 
                 275 
                 272 
                 276 
                 271 
                 277 
                 270 
                 278 
                 284 
                 283 
                 285 
                 282 
                 286 
                 281 
                 287 
                 280 
                 288 
               
               
                   
               
             
          
         
       
     
         [0105]    As like the tables 1˜5, in the tables 6-8, 1 RB and 2 RB length sequence are not shown because 1 RB and 2 RB length sequence are differently defined. 
         [0106]    In another embodiment of this invention, the maximum number of sequences per each group can be predetermined for various reasons. The following tables 9 and 10 show the example of the case when the maximum number of sequences per group is limited to 5 sequences. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
             
             
               
                 Gr. 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Idx 
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 2 
                 2 
                 3 
                 3 
                 2 
                 3 
                 4 
                 2 
                 4 
                 3 
                 5 
               
               
                 2 
                 2 
                 3 
                 4 
                 5 
                 4 
                 6 
                 5 
                 7 
                 6 
                 8 
                 7 
                 8 
                 6 
               
               
                 3 
                 3 
                 5 
                 6 
                 7 
                 6 
                 9 
                 8 
                 10 
                 11 
                 9 
                 11 
                 10 
                 12 
               
               
                 4 
                 4 
                 6 
                 8 
                 9 
                 10 
                 11 
                 12 
                 14 
                 13 
                 15 
                 15 
                 14 
                 16 
               
               
                 5 
                 5 
                 8 
                 10 
                 11 
                 12 
                 14 
                 15 
                 17 
                 18 
                 16 
                 18 
                 19 
                 17 
               
               
                 6 
                 6 
                 9 
                 11 
                 14 
                 13 
                 17 
                 18 
                 21 
                 20 
                 22 
                 22 
                 21 
                 23 
               
               
                 7 
                 7 
                 11 
                 13 
                 16 
                 17 
                 20 
                 21 
                 24 
                 25 
                 23 
                 26 
                 25 
                 27 
               
               
                 8 
                 8 
                 12 
                 15 
                 18 
                 19 
                 23 
                 22 
                 28 
                 27 
                 29 
                 29 
                 30 
                 28 
               
               
                 9 
                 9 
                 14 
                 17 
                 21 
                 20 
                 26 
                 25 
                 31 
                 32 
                 30 
                 33 
                 32 
                 34 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 22 
                 29 
                 28 
                 35 
                 34 
                 36 
                 36 
                 37 
                 35 
               
               
                 11 
                 11 
                 17 
                 21 
                 25 
                 26 
                 32 
                 31 
                 38 
                 37 
                 39 
                 40 
                 41 
                 39 
               
               
                 12 
                 12 
                 18 
                 23 
                 27 
                 28 
                 34 
                 35 
                 41 
                 42 
                 40 
                 44 
                 43 
                 45 
               
               
                 13 
                 13 
                 20 
                 25 
                 30 
                 29 
                 37 
                 38 
                 45 
                 44 
                 46 
                 47 
                 48 
                 46 
               
               
                 14 
                 14 
                 21 
                 27 
                 32 
                 33 
                 40 
                 41 
                 48 
                 49 
                 47 
                 51 
                 52 
                 50 
               
               
                 15 
                 15 
                 23 
                 29 
                 34 
                 35 
                 43 
                 44 
                 52 
                 51 
                 53 
                 55 
                 54 
                 56 
               
               
                 16 
                 16 
                 24 
                 30 
                 37 
                 36 
                 46 
                 45 
                 55 
                 56 
                 54 
                 58 
                 59 
                 57 
               
               
                 17 
                 17 
                 26 
                 32 
                 39 
                 38 
                 49 
                 48 
                 59 
                 58 
                 60 
                 62 
                 61 
                 63 
               
               
                 18 
                 18 
                 27 
                 34 
                 41 
                 42 
                 52 
                 51 
                 62 
                 63 
                 61 
                 66 
                 65 
                 67 
               
               
                 19 
                 19 
                 29 
                 36 
                 44 
                 43 
                 55 
                 54 
                 66 
                 65 
                 67 
                 69 
                 70 
                 68 
               
               
                 20 
                 20 
                 30 
                 38 
                 46 
                 45 
                 57 
                 58 
                 69 
                 70 
                 68 
                 73 
                 72 
                 74 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 49 
                 60 
                 61 
                 72 
                 73 
                 71 
                 77 
                 76 
                 78 
               
               
                 22 
                 22 
                 33 
                 42 
                 50 
                 51 
                 63 
                 64 
                 76 
                 75 
                 77 
                 80 
                 81 
                 79 
               
               
                 23 
                 23 
                 35 
                 44 
                 53 
                 52 
                 66 
                 67 
                 79 
                 80 
                 78 
                 84 
                 83 
                 85 
               
               
                 24 
                 24 
                 36 
                 46 
                 55 
                 54 
                 69 
                 68 
                 83 
                 82 
                 84 
                 87 
                 88 
                 86 
               
               
                 25 
                 25 
                 38 
                 48 
                 57 
                 58 
                 72 
                 71 
                 86 
                 87 
                 85 
                 91 
                 92 
                 90 
               
               
                 26 
                 26 
                 39 
                 49 
                 60 
                 59 
                 75 
                 74 
                 90 
                 89 
                 91 
                 95 
                 94 
                 96 
               
               
                 27 
                 27 
                 41 
                 51 
                 62 
                 61 
                 78 
                 77 
                 93 
                 94 
                 92 
                 98 
                 99 
                 97 
               
               
                 28 
                 28 
                 42 
                 53 
                 64 
                 65 
                 80 
                 81 
                 97 
                 96 
                 98 
                 102 
                 103 
                 101 
               
               
                 29 
                 29 
                 44 
                 55 
                 66 
                 67 
                 83 
                 84 
                 100 
                 101 
                 99 
                 106 
                 105 
                 107 
               
               
                 30 
                 30 
                 45 
                 57 
                 69 
                 68 
                 86 
                 87 
                 104 
                 103 
                 105 
                 109 
                 110 
                 108 
               
               
                   
               
             
          
           
               
                   
                 Gr. 
                   
                   
               
               
                   
                 Idx 
                   
                   
               
               
                   
                 3RBs 
                 12RB 
                 15RB 
               
               
                   
               
             
          
           
               
                   
                 1 
                 4 
                 5 
                 3 
                 6 
                 6 
                 5 
                 7 
                 4 
                 8 
               
               
                   
                 2 
                 9 
                 8 
                 10 
                 7 
                 12 
                 11 
                 13 
                 10 
                 14 
               
               
                   
                 3 
                 13 
                 14 
                 12 
                 15 
                 17 
                 18 
                 16 
                 19 
                 15 
               
               
                   
                 4 
                 18 
                 17 
                 19 
                 16 
                 23 
                 24 
                 22 
                 25 
                 21 
               
               
                   
                 5 
                 22 
                 23 
                 21 
                 24 
                 29 
                 28 
                 30 
                 27 
                 31 
               
               
                   
                 6 
                 27 
                 26 
                 28 
                 25 
                 35 
                 34 
                 36 
                 33 
                 37 
               
               
                   
                 7 
                 31 
                 32 
                 30 
                 33 
                 40 
                 41 
                 39 
                 42 
                 38 
               
               
                   
                 8 
                 36 
                 35 
                 37 
                 34 
                 46 
                 47 
                 45 
                 48 
                 44 
               
               
                   
                 9 
                 40 
                 41 
                 39 
                 42 
                 52 
                 51 
                 53 
                 50 
                 54 
               
               
                   
                 10 
                 45 
                 44 
                 46 
                 43 
                 58 
                 57 
                 59 
                 56 
                 60 
               
               
                   
                 11 
                 49 
                 50 
                 48 
                 51 
                 64 
                 63 
                 65 
                 62 
                 66 
               
               
                   
                 12 
                 54 
                 53 
                 55 
                 52 
                 69 
                 70 
                 68 
                 71 
                 67 
               
               
                   
                 13 
                 58 
                 59 
                 57 
                 60 
                 75 
                 76 
                 74 
                 77 
                 73 
               
               
                   
                 14 
                 63 
                 62 
                 64 
                 61 
                 81 
                 80 
                 82 
                 79 
                 83 
               
               
                   
                 15 
                 67 
                 68 
                 66 
                 69 
                 87 
                 86 
                 88 
                 85 
                 89 
               
               
                   
                 16 
                 72 
                 71 
                 73 
                 70 
                 92 
                 93 
                 91 
                 94 
                 90 
               
               
                   
                 17 
                 76 
                 77 
                 75 
                 78 
                 98 
                 99 
                 97 
                 100 
                 96 
               
               
                   
                 18 
                 81 
                 80 
                 82 
                 79 
                 104 
                 103 
                 105 
                 102 
                 106 
               
               
                   
                 19 
                 85 
                 86 
                 84 
                 87 
                 110 
                 109 
                 111 
                 108 
                 112 
               
               
                   
                 20 
                 90 
                 89 
                 91 
                 88 
                 115 
                 116 
                 114 
                 117 
                 113 
               
               
                   
                 21 
                 94 
                 95 
                 93 
                 96 
                 121 
                 122 
                 120 
                 123 
                 119 
               
               
                   
                 22 
                 99 
                 98 
                 100 
                 97 
                 127 
                 128 
                 126 
                 129 
                 125 
               
               
                   
                 23 
                 103 
                 104 
                 102 
                 105 
                 133 
                 132 
                 134 
                 131 
                 135 
               
               
                   
                 24 
                 108 
                 107 
                 109 
                 106 
                 139 
                 138 
                 140 
                 137 
                 141 
               
               
                   
                 25 
                 112 
                 113 
                 111 
                 114 
                 144 
                 145 
                 143 
                 146 
                 142 
               
               
                   
                 26 
                 117 
                 116 
                 118 
                 115 
                 150 
                 151 
                 149 
                 152 
                 148 
               
               
                   
                 27 
                 121 
                 122 
                 120 
                 123 
                 156 
                 155 
                 157 
                 154 
                 158 
               
               
                   
                 28 
                 126 
                 125 
                 127 
                 124 
                 162 
                 161 
                 163 
                 160 
                 164 
               
               
                   
                 29 
                 130 
                 131 
                 129 
                 132 
                 167 
                 168 
                 166 
                 169 
                 165 
               
               
                   
                 30 
                 135 
                 134 
                 136 
                 133 
                 173 
                 174 
                 172 
                 175 
                 171 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
             
             
               
                 Group index 
                   
                   
                   
               
               
                 based on 3RBs 
                 16RB 
                 18RB 
                 20RB 
               
               
                   
               
             
          
           
               
                 1 
                 6 
                 7 
                 5 
                 8 
                 4 
                 7 
                 6 
                 8 
                 5 
                 9 
                 8 
                 7 
                 9 
                 6 
                 10 
               
               
                 2 
                 12 
                 13 
                 11 
                 14 
                 10 
                 14 
                 13 
                 15 
                 12 
                 16 
                 15 
                 16 
                 14 
                 17 
                 13 
               
               
                 3 
                 18 
                 19 
                 17 
                 20 
                 16 
                 20 
                 21 
                 19 
                 22 
                 18 
                 23 
                 24 
                 22 
                 25 
                 21 
               
               
                 4 
                 25 
                 24 
                 26 
                 23 
                 27 
                 27 
                 28 
                 26 
                 29 
                 25 
                 31 
                 30 
                 32 
                 29 
                 33 
               
               
                 5 
                 31 
                 30 
                 32 
                 29 
                 33 
                 34 
                 35 
                 33 
                 36 
                 32 
                 39 
                 38 
                 40 
                 37 
                 41 
               
               
                 6 
                 37 
                 36 
                 38 
                 35 
                 39 
                 41 
                 40 
                 42 
                 39 
                 43 
                 46 
                 47 
                 45 
                 48 
                 44 
               
               
                 7 
                 43 
                 44 
                 42 
                 45 
                 41 
                 48 
                 47 
                 49 
                 46 
                 50 
                 54 
                 53 
                 55 
                 52 
                 56 
               
               
                 8 
                 49 
                 50 
                 48 
                 51 
                 47 
                 54 
                 55 
                 53 
                 56 
                 52 
                 62 
                 61 
                 63 
                 60 
                 64 
               
               
                 9 
                 55 
                 56 
                 54 
                 57 
                 53 
                 61 
                 62 
                 60 
                 63 
                 59 
                 69 
                 70 
                 68 
                 71 
                 67 
               
               
                 10 
                 62 
                 61 
                 63 
                 60 
                 64 
                 68 
                 69 
                 67 
                 70 
                 66 
                 77 
                 78 
                 76 
                 79 
                 75 
               
               
                 11 
                 68 
                 67 
                 69 
                 66 
                 70 
                 75 
                 74 
                 76 
                 73 
                 77 
                 85 
                 84 
                 86 
                 83 
                 87 
               
               
                 12 
                 74 
                 73 
                 75 
                 72 
                 76 
                 82 
                 81 
                 83 
                 80 
                 84 
                 93 
                 92 
                 94 
                 91 
                 95 
               
               
                 13 
                 80 
                 81 
                 79 
                 82 
                 78 
                 88 
                 89 
                 87 
                 90 
                 86 
                 100 
                 101 
                 99 
                 102 
                 98 
               
               
                 14 
                 86 
                 87 
                 85 
                 88 
                 84 
                 95 
                 96 
                 94 
                 97 
                 93 
                 108 
                 107 
                 109 
                 106 
                 110 
               
               
                 15 
                 92 
                 93 
                 91 
                 94 
                 90 
                 102 
                 103 
                 101 
                 104 
                 100 
                 116 
                 115 
                 117 
                 114 
                 118 
               
               
                 16 
                 99 
                 98 
                 100 
                 97 
                 101 
                 109 
                 108 
                 110 
                 107 
                 111 
                 123 
                 124 
                 122 
                 125 
                 121 
               
               
                 17 
                 105 
                 104 
                 106 
                 103 
                 107 
                 116 
                 115 
                 117 
                 114 
                 118 
                 131 
                 132 
                 130 
                 133 
                 129 
               
               
                 18 
                 111 
                 110 
                 112 
                 109 
                 113 
                 123 
                 122 
                 124 
                 121 
                 125 
                 139 
                 138 
                 140 
                 137 
                 141 
               
               
                 19 
                 117 
                 118 
                 116 
                 119 
                 115 
                 129 
                 130 
                 128 
                 131 
                 127 
                 146 
                 147 
                 145 
                 148 
                 144 
               
               
                 20 
                 123 
                 124 
                 122 
                 125 
                 121 
                 136 
                 137 
                 135 
                 138 
                 134 
                 154 
                 155 
                 153 
                 156 
                 152 
               
               
                 21 
                 129 
                 130 
                 128 
                 131 
                 127 
                 143 
                 142 
                 144 
                 141 
                 145 
                 162 
                 161 
                 163 
                 160 
                 164 
               
               
                 22 
                 136 
                 135 
                 137 
                 134 
                 138 
                 150 
                 149 
                 151 
                 148 
                 152 
                 170 
                 169 
                 171 
                 168 
                 172 
               
               
                 23 
                 142 
                 141 
                 143 
                 140 
                 144 
                 157 
                 156 
                 158 
                 155 
                 159 
                 177 
                 178 
                 176 
                 179 
                 175 
               
               
                 24 
                 148 
                 147 
                 149 
                 146 
                 150 
                 163 
                 164 
                 162 
                 165 
                 161 
                 185 
                 186 
                 184 
                 187 
                 183 
               
               
                 25 
                 154 
                 155 
                 153 
                 156 
                 152 
                 170 
                 171 
                 169 
                 172 
                 168 
                 193 
                 192 
                 194 
                 191 
                 195 
               
               
                 26 
                 160 
                 161 
                 159 
                 162 
                 158 
                 177 
                 176 
                 178 
                 175 
                 179 
                 200 
                 201 
                 199 
                 202 
                 198 
               
               
                 27 
                 166 
                 167 
                 165 
                 168 
                 164 
                 184 
                 183 
                 185 
                 182 
                 186 
                 208 
                 209 
                 207 
                 210 
                 206 
               
               
                 28 
                 173 
                 172 
                 174 
                 171 
                 175 
                 191 
                 190 
                 192 
                 189 
                 193 
                 216 
                 215 
                 217 
                 214 
                 218 
               
               
                 29 
                 179 
                 178 
                 180 
                 177 
                 181 
                 197 
                 198 
                 196 
                 199 
                 195 
                 224 
                 223 
                 225 
                 222 
                 226 
               
               
                 30 
                 185 
                 184 
                 186 
                 183 
                 187 
                 204 
                 205 
                 203 
                 206 
                 202 
                 231 
                 232 
                 230 
                 233 
                 229 
               
               
                   
               
             
          
           
               
                   
                 Group index 
                   
                   
               
               
                   
                 based on 3RBs 
                 24RB 
                 25RBs 
               
               
                   
               
             
          
           
               
                   
                 1 
                 9 
                 10 
                 8 
                 11 
                 7 
                 9 
                 10 
                 8 
                 11 
                 7 
               
               
                   
                 2 
                 18 
                 19 
                 17 
                 20 
                 16 
                 19 
                 18 
                 20 
                 17 
                 21 
               
               
                   
                 3 
                 27 
                 28 
                 26 
                 29 
                 25 
                 28 
                 29 
                 27 
                 30 
                 26 
               
               
                   
                 4 
                 37 
                 36 
                 38 
                 35 
                 39 
                 38 
                 37 
                 39 
                 36 
                 40 
               
               
                   
                 5 
                 46 
                 45 
                 47 
                 44 
                 48 
                 47 
                 48 
                 46 
                 49 
                 45 
               
               
                   
                 6 
                 55 
                 54 
                 56 
                 53 
                 57 
                 57 
                 56 
                 58 
                 55 
                 59 
               
               
                   
                 7 
                 64 
                 63 
                 65 
                 62 
                 66 
                 66 
                 67 
                 65 
                 68 
                 64 
               
               
                   
                 8 
                 73 
                 74 
                 72 
                 75 
                 71 
                 76 
                 75 
                 77 
                 74 
                 78 
               
               
                   
                 9 
                 82 
                 83 
                 81 
                 84 
                 80 
                 85 
                 86 
                 84 
                 87 
                 83 
               
               
                   
                 10 
                 91 
                 92 
                 90 
                 93 
                 89 
                 95 
                 94 
                 96 
                 93 
                 97 
               
               
                   
                 11 
                 100 
                 101 
                 99 
                 102 
                 98 
                 104 
                 103 
                 105 
                 102 
                 106 
               
               
                   
                 12 
                 110 
                 109 
                 111 
                 108 
                 112 
                 113 
                 114 
                 112 
                 115 
                 111 
               
               
                   
                 13 
                 119 
                 118 
                 120 
                 117 
                 121 
                 123 
                 122 
                 124 
                 121 
                 125 
               
               
                   
                 14 
                 128 
                 127 
                 129 
                 126 
                 130 
                 132 
                 133 
                 131 
                 134 
                 130 
               
               
                   
                 15 
                 137 
                 136 
                 138 
                 135 
                 139 
                 142 
                 141 
                 143 
                 140 
                 144 
               
               
                   
                 16 
                 146 
                 147 
                 145 
                 148 
                 144 
                 151 
                 152 
                 150 
                 153 
                 149 
               
               
                   
                 17 
                 155 
                 156 
                 154 
                 157 
                 153 
                 161 
                 160 
                 162 
                 159 
                 163 
               
               
                   
                 18 
                 164 
                 165 
                 163 
                 166 
                 162 
                 170 
                 171 
                 169 
                 172 
                 168 
               
               
                   
                 19 
                 173 
                 174 
                 172 
                 175 
                 171 
                 180 
                 179 
                 181 
                 178 
                 182 
               
               
                   
                 20 
                 183 
                 182 
                 184 
                 181 
                 185 
                 189 
                 190 
                 188 
                 191 
                 187 
               
               
                   
                 21 
                 192 
                 191 
                 193 
                 190 
                 194 
                 198 
                 199 
                 197 
                 200 
                 196 
               
               
                   
                 22 
                 201 
                 200 
                 202 
                 199 
                 203 
                 208 
                 207 
                 209 
                 206 
                 210 
               
               
                   
                 23 
                 210 
                 209 
                 211 
                 208 
                 212 
                 217 
                 218 
                 216 
                 219 
                 215 
               
               
                   
                 24 
                 219 
                 220 
                 218 
                 221 
                 217 
                 227 
                 226 
                 228 
                 225 
                 229 
               
               
                   
                 25 
                 228 
                 229 
                 227 
                 230 
                 226 
                 236 
                 237 
                 235 
                 238 
                 234 
               
               
                   
                 26 
                 237 
                 238 
                 236 
                 239 
                 235 
                 246 
                 245 
                 247 
                 244 
                 248 
               
               
                   
                 27 
                 246 
                 247 
                 245 
                 248 
                 244 
                 255 
                 256 
                 254 
                 257 
                 253 
               
               
                   
                 28 
                 256 
                 255 
                 257 
                 254 
                 258 
                 265 
                 264 
                 266 
                 263 
                 267 
               
               
                   
                 29 
                 265 
                 264 
                 266 
                 263 
                 267 
                 274 
                 275 
                 273 
                 276 
                 272 
               
               
                   
                 30 
                 274 
                 273 
                 275 
                 272 
                 276 
                 284 
                 283 
                 285 
                 282 
                 286 
               
               
                   
               
             
          
         
       
     
         [0107]    And, in another example, the maximum number of sequences can be predetermined to 4. The following tables 11 and 12 show this case. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
             
             
               
                 Group index 
                   
                   
                   
                   
                   
                   
                   
               
               
                 based on 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 2 
                 2 
                 3 
                 3 
                 2 
                 3 
                 4 
                 2 
                 4 
                 3 
                 5 
               
               
                 2 
                 2 
                 3 
                 4 
                 5 
                 4 
                 6 
                 5 
                 7 
                 6 
                 8 
                 7 
                 8 
                 6 
               
               
                 3 
                 3 
                 5 
                 6 
                 7 
                 6 
                 9 
                 8 
                 10 
                 11 
                 9 
                 11 
                 10 
                 12 
               
               
                 4 
                 4 
                 6 
                 8 
                 9 
                 10 
                 11 
                 12 
                 14 
                 13 
                 15 
                 15 
                 14 
                 16 
               
               
                 5 
                 5 
                 8 
                 10 
                 11 
                 12 
                 14 
                 15 
                 17 
                 18 
                 16 
                 18 
                 19 
                 17 
               
               
                 6 
                 6 
                 9 
                 11 
                 14 
                 13 
                 17 
                 18 
                 21 
                 20 
                 22 
                 22 
                 21 
                 23 
               
               
                 7 
                 7 
                 11 
                 13 
                 16 
                 17 
                 20 
                 21 
                 24 
                 25 
                 23 
                 26 
                 25 
                 27 
               
               
                 8 
                 8 
                 12 
                 15 
                 18 
                 19 
                 23 
                 22 
                 28 
                 27 
                 29 
                 29 
                 30 
                 28 
               
               
                 9 
                 9 
                 14 
                 17 
                 21 
                 20 
                 26 
                 25 
                 31 
                 32 
                 30 
                 33 
                 32 
                 34 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 22 
                 29 
                 28 
                 35 
                 34 
                 36 
                 36 
                 37 
                 35 
               
               
                 11 
                 11 
                 17 
                 21 
                 25 
                 26 
                 32 
                 31 
                 38 
                 37 
                 39 
                 40 
                 41 
                 39 
               
               
                 12 
                 12 
                 18 
                 23 
                 27 
                 28 
                 34 
                 35 
                 41 
                 42 
                 40 
                 44 
                 43 
                 45 
               
               
                 13 
                 13 
                 20 
                 25 
                 30 
                 29 
                 37 
                 38 
                 45 
                 44 
                 46 
                 47 
                 48 
                 46 
               
               
                 14 
                 14 
                 21 
                 27 
                 32 
                 33 
                 40 
                 41 
                 48 
                 49 
                 47 
                 51 
                 52 
                 50 
               
               
                 15 
                 15 
                 23 
                 29 
                 34 
                 35 
                 43 
                 44 
                 52 
                 51 
                 53 
                 55 
                 54 
                 56 
               
               
                 16 
                 16 
                 24 
                 30 
                 37 
                 36 
                 46 
                 45 
                 55 
                 56 
                 54 
                 58 
                 59 
                 57 
               
               
                 17 
                 17 
                 26 
                 32 
                 39 
                 38 
                 49 
                 48 
                 59 
                 58 
                 60 
                 62 
                 61 
                 63 
               
               
                 18 
                 18 
                 27 
                 34 
                 41 
                 42 
                 52 
                 51 
                 62 
                 63 
                 61 
                 66 
                 65 
                 67 
               
               
                 19 
                 19 
                 29 
                 36 
                 44 
                 43 
                 55 
                 54 
                 66 
                 65 
                 67 
                 69 
                 70 
                 68 
               
               
                 20 
                 20 
                 30 
                 38 
                 46 
                 45 
                 57 
                 58 
                 69 
                 70 
                 68 
                 73 
                 72 
                 74 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 49 
                 60 
                 61 
                 72 
                 73 
                 71 
                 77 
                 76 
                 78 
               
               
                 22 
                 22 
                 33 
                 42 
                 50 
                 51 
                 63 
                 64 
                 76 
                 75 
                 77 
                 80 
                 81 
                 79 
               
               
                 23 
                 23 
                 35 
                 44 
                 53 
                 52 
                 66 
                 67 
                 79 
                 80 
                 78 
                 84 
                 83 
                 85 
               
               
                 24 
                 24 
                 36 
                 46 
                 55 
                 54 
                 69 
                 68 
                 83 
                 82 
                 84 
                 87 
                 88 
                 86 
               
               
                 25 
                 25 
                 38 
                 48 
                 57 
                 58 
                 72 
                 71 
                 86 
                 87 
                 85 
                 91 
                 92 
                 90 
               
               
                 26 
                 26 
                 39 
                 49 
                 60 
                 59 
                 75 
                 74 
                 90 
                 89 
                 91 
                 95 
                 94 
                 96 
               
               
                 27 
                 27 
                 41 
                 51 
                 62 
                 61 
                 78 
                 77 
                 93 
                 94 
                 92 
                 98 
                 99 
                 97 
               
               
                 28 
                 28 
                 42 
                 53 
                 64 
                 65 
                 80 
                 81 
                 97 
                 96 
                 98 
                 102 
                 103 
                 101 
               
               
                 29 
                 29 
                 44 
                 55 
                 66 
                 67 
                 83 
                 84 
                 100 
                 101 
                 99 
                 106 
                 105 
                 107 
               
               
                 30 
                 30 
                 45 
                 57 
                 69 
                 68 
                 86 
                 87 
                 104 
                 103 
                 105 
                 109 
                 110 
                 108 
               
               
                   
               
             
          
           
               
                   
                 Group index 
                   
                   
               
               
                   
                 based on 3RBs 
                 12RB 
                 15RB 
               
               
                   
               
             
          
           
               
                   
                 1 
                 4 
                 5 
                 3 
                 6 
                 6 
                 5 
                 7 
                 4 
               
               
                   
                 2 
                 9 
                 8 
                 10 
                 7 
                 12 
                 11 
                 13 
                 10 
               
               
                   
                 3 
                 13 
                 14 
                 12 
                 15 
                 17 
                 18 
                 16 
                 19 
               
               
                   
                 4 
                 18 
                 17 
                 19 
                 16 
                 23 
                 24 
                 22 
                 25 
               
               
                   
                 5 
                 22 
                 23 
                 21 
                 24 
                 29 
                 28 
                 30 
                 27 
               
               
                   
                 6 
                 27 
                 26 
                 28 
                 25 
                 35 
                 34 
                 36 
                 33 
               
               
                   
                 7 
                 31 
                 32 
                 30 
                 33 
                 40 
                 41 
                 39 
                 42 
               
               
                   
                 8 
                 36 
                 35 
                 37 
                 34 
                 46 
                 47 
                 45 
                 48 
               
               
                   
                 9 
                 40 
                 41 
                 39 
                 42 
                 52 
                 51 
                 53 
                 50 
               
               
                   
                 10 
                 45 
                 44 
                 46 
                 43 
                 58 
                 57 
                 59 
                 56 
               
               
                   
                 11 
                 49 
                 50 
                 48 
                 51 
                 64 
                 63 
                 65 
                 62 
               
               
                   
                 12 
                 54 
                 53 
                 55 
                 52 
                 69 
                 70 
                 68 
                 71 
               
               
                   
                 13 
                 58 
                 59 
                 57 
                 60 
                 75 
                 76 
                 74 
                 77 
               
               
                   
                 14 
                 63 
                 62 
                 64 
                 61 
                 81 
                 80 
                 82 
                 79 
               
               
                   
                 15 
                 67 
                 68 
                 66 
                 69 
                 87 
                 86 
                 88 
                 85 
               
               
                   
                 16 
                 72 
                 71 
                 73 
                 70 
                 92 
                 93 
                 91 
                 94 
               
               
                   
                 17 
                 76 
                 77 
                 75 
                 78 
                 98 
                 99 
                 97 
                 100 
               
               
                   
                 18 
                 81 
                 80 
                 82 
                 79 
                 104 
                 103 
                 105 
                 102 
               
               
                   
                 19 
                 85 
                 86 
                 84 
                 87 
                 110 
                 109 
                 111 
                 108 
               
               
                   
                 20 
                 90 
                 89 
                 91 
                 88 
                 115 
                 116 
                 114 
                 117 
               
               
                   
                 21 
                 94 
                 95 
                 93 
                 96 
                 121 
                 122 
                 120 
                 123 
               
               
                   
                 22 
                 99 
                 98 
                 100 
                 97 
                 127 
                 128 
                 126 
                 129 
               
               
                   
                 23 
                 103 
                 104 
                 102 
                 105 
                 133 
                 132 
                 134 
                 131 
               
               
                   
                 24 
                 108 
                 107 
                 109 
                 106 
                 139 
                 138 
                 140 
                 137 
               
               
                   
                 25 
                 112 
                 113 
                 111 
                 114 
                 144 
                 145 
                 143 
                 146 
               
               
                   
                 26 
                 117 
                 116 
                 118 
                 115 
                 150 
                 151 
                 149 
                 152 
               
               
                   
                 27 
                 121 
                 122 
                 120 
                 123 
                 156 
                 155 
                 157 
                 154 
               
               
                   
                 28 
                 126 
                 125 
                 127 
                 124 
                 162 
                 161 
                 163 
                 160 
               
               
                   
                 29 
                 130 
                 131 
                 129 
                 132 
                 167 
                 168 
                 166 
                 169 
               
               
                   
                 30 
                 135 
                 134 
                 136 
                 133 
                 173 
                 174 
                 172 
                 175 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
               
                   
               
             
             
               
                 Group index 
                   
                   
                   
               
               
                 based on 3RBs 
                 16RB 
                 18RB 
                 20RB 
               
               
                   
               
             
          
           
               
                 1 
                 6 
                 7 
                 5 
                 8 
                 7 
                 6 
                 8 
                 5 
                 8 
                 7 
                 9 
                 6 
               
               
                 2 
                 12 
                 13 
                 11 
                 14 
                 14 
                 13 
                 15 
                 12 
                 15 
                 16 
                 14 
                 17 
               
               
                 3 
                 18 
                 19 
                 17 
                 20 
                 20 
                 21 
                 19 
                 22 
                 23 
                 24 
                 22 
                 25 
               
               
                 4 
                 25 
                 24 
                 26 
                 23 
                 27 
                 28 
                 26 
                 29 
                 31 
                 30 
                 32 
                 29 
               
               
                 5 
                 31 
                 30 
                 32 
                 29 
                 34 
                 35 
                 33 
                 36 
                 39 
                 38 
                 40 
                 37 
               
               
                 6 
                 37 
                 36 
                 38 
                 35 
                 41 
                 40 
                 42 
                 39 
                 46 
                 47 
                 45 
                 48 
               
               
                 7 
                 43 
                 44 
                 42 
                 45 
                 48 
                 47 
                 49 
                 46 
                 54 
                 53 
                 55 
                 52 
               
               
                 8 
                 49 
                 50 
                 48 
                 51 
                 54 
                 55 
                 53 
                 56 
                 62 
                 61 
                 63 
                 60 
               
               
                 9 
                 55 
                 56 
                 54 
                 57 
                 61 
                 62 
                 60 
                 63 
                 69 
                 70 
                 68 
                 71 
               
               
                 10 
                 62 
                 61 
                 63 
                 60 
                 68 
                 69 
                 67 
                 70 
                 77 
                 78 
                 76 
                 79 
               
               
                 11 
                 68 
                 67 
                 69 
                 66 
                 75 
                 74 
                 76 
                 73 
                 85 
                 84 
                 86 
                 83 
               
               
                 12 
                 74 
                 73 
                 75 
                 72 
                 82 
                 81 
                 83 
                 80 
                 93 
                 92 
                 94 
                 91 
               
               
                 13 
                 80 
                 81 
                 79 
                 82 
                 88 
                 89 
                 87 
                 90 
                 100 
                 101 
                 99 
                 102 
               
               
                 14 
                 86 
                 87 
                 85 
                 88 
                 95 
                 96 
                 94 
                 97 
                 108 
                 107 
                 109 
                 106 
               
               
                 15 
                 92 
                 93 
                 91 
                 94 
                 102 
                 103 
                 101 
                 104 
                 116 
                 115 
                 117 
                 114 
               
               
                 16 
                 99 
                 98 
                 100 
                 97 
                 109 
                 108 
                 110 
                 107 
                 123 
                 124 
                 122 
                 125 
               
               
                 17 
                 105 
                 104 
                 106 
                 103 
                 116 
                 115 
                 117 
                 114 
                 131 
                 132 
                 130 
                 133 
               
               
                 18 
                 111 
                 110 
                 112 
                 109 
                 123 
                 122 
                 124 
                 121 
                 139 
                 138 
                 140 
                 137 
               
               
                 19 
                 117 
                 118 
                 116 
                 119 
                 129 
                 130 
                 128 
                 131 
                 146 
                 147 
                 145 
                 148 
               
               
                 20 
                 123 
                 124 
                 122 
                 125 
                 136 
                 137 
                 135 
                 138 
                 154 
                 155 
                 153 
                 156 
               
               
                 21 
                 129 
                 130 
                 128 
                 131 
                 143 
                 142 
                 144 
                 141 
                 162 
                 161 
                 163 
                 160 
               
               
                 22 
                 136 
                 135 
                 137 
                 134 
                 150 
                 149 
                 151 
                 148 
                 170 
                 169 
                 171 
                 168 
               
               
                 23 
                 142 
                 141 
                 143 
                 140 
                 157 
                 156 
                 158 
                 155 
                 177 
                 178 
                 176 
                 179 
               
               
                 24 
                 148 
                 147 
                 149 
                 146 
                 163 
                 164 
                 162 
                 165 
                 185 
                 186 
                 184 
                 187 
               
               
                 25 
                 154 
                 155 
                 153 
                 156 
                 170 
                 171 
                 169 
                 172 
                 193 
                 192 
                 194 
                 191 
               
               
                 26 
                 160 
                 161 
                 159 
                 162 
                 177 
                 176 
                 178 
                 175 
                 200 
                 201 
                 199 
                 202 
               
               
                 27 
                 166 
                 167 
                 165 
                 168 
                 184 
                 183 
                 185 
                 182 
                 208 
                 209 
                 207 
                 210 
               
               
                 28 
                 173 
                 172 
                 174 
                 171 
                 191 
                 190 
                 192 
                 189 
                 216 
                 215 
                 217 
                 214 
               
               
                 29 
                 179 
                 178 
                 180 
                 177 
                 197 
                 198 
                 196 
                 199 
                 224 
                 223 
                 225 
                 222 
               
               
                 30 
                 185 
                 184 
                 186 
                 183 
                 204 
                 205 
                 203 
                 206 
                 231 
                 232 
                 230 
                 233 
               
               
                   
               
             
          
           
               
                   
                 Group index 
                   
                   
               
               
                   
                 based on 3RBs 
                 24RB 
                 25RBs 
               
               
                   
               
             
          
           
               
                   
                 1 
                 9 
                 10 
                 8 
                 11 
                 9 
                 10 
                 8 
                 11 
               
               
                   
                 2 
                 18 
                 19 
                 17 
                 20 
                 19 
                 18 
                 20 
                 17 
               
               
                   
                 3 
                 27 
                 28 
                 26 
                 29 
                 28 
                 29 
                 27 
                 30 
               
               
                   
                 4 
                 37 
                 36 
                 38 
                 35 
                 38 
                 37 
                 39 
                 36 
               
               
                   
                 5 
                 46 
                 45 
                 47 
                 44 
                 47 
                 48 
                 46 
                 49 
               
               
                   
                 6 
                 55 
                 54 
                 56 
                 53 
                 57 
                 56 
                 58 
                 55 
               
               
                   
                 7 
                 64 
                 63 
                 65 
                 62 
                 66 
                 67 
                 65 
                 68 
               
               
                   
                 8 
                 73 
                 74 
                 72 
                 75 
                 76 
                 75 
                 77 
                 74 
               
               
                   
                 9 
                 82 
                 83 
                 81 
                 84 
                 85 
                 86 
                 84 
                 87 
               
               
                   
                 10 
                 91 
                 92 
                 90 
                 93 
                 95 
                 94 
                 96 
                 93 
               
               
                   
                 11 
                 100 
                 101 
                 99 
                 102 
                 104 
                 103 
                 105 
                 102 
               
               
                   
                 12 
                 110 
                 109 
                 111 
                 108 
                 113 
                 114 
                 112 
                 115 
               
               
                   
                 13 
                 119 
                 118 
                 120 
                 117 
                 123 
                 122 
                 124 
                 121 
               
               
                   
                 14 
                 128 
                 127 
                 129 
                 126 
                 132 
                 133 
                 131 
                 134 
               
               
                   
                 15 
                 137 
                 136 
                 138 
                 135 
                 142 
                 141 
                 143 
                 140 
               
               
                   
                 16 
                 146 
                 147 
                 145 
                 148 
                 151 
                 152 
                 150 
                 153 
               
               
                   
                 17 
                 155 
                 156 
                 154 
                 157 
                 161 
                 160 
                 162 
                 159 
               
               
                   
                 18 
                 164 
                 165 
                 163 
                 166 
                 170 
                 171 
                 169 
                 172 
               
               
                   
                 19 
                 173 
                 174 
                 172 
                 175 
                 180 
                 179 
                 181 
                 178 
               
               
                   
                 20 
                 183 
                 182 
                 184 
                 181 
                 189 
                 190 
                 188 
                 191 
               
               
                   
                 21 
                 192 
                 191 
                 193 
                 190 
                 198 
                 199 
                 197 
                 200 
               
               
                   
                 22 
                 201 
                 200 
                 202 
                 199 
                 208 
                 207 
                 209 
                 206 
               
               
                   
                 23 
                 210 
                 209 
                 211 
                 208 
                 217 
                 218 
                 216 
                 219 
               
               
                   
                 24 
                 219 
                 220 
                 218 
                 221 
                 227 
                 226 
                 228 
                 225 
               
               
                   
                 25 
                 228 
                 229 
                 227 
                 230 
                 236 
                 237 
                 235 
                 238 
               
               
                   
                 26 
                 237 
                 238 
                 236 
                 239 
                 246 
                 245 
                 247 
                 244 
               
               
                   
                 27 
                 246 
                 247 
                 245 
                 248 
                 255 
                 256 
                 254 
                 257 
               
               
                   
                 28 
                 256 
                 255 
                 257 
                 254 
                 265 
                 264 
                 266 
                 263 
               
               
                   
                 29 
                 265 
                 264 
                 266 
                 263 
                 274 
                 275 
                 273 
                 276 
               
               
                   
                 30 
                 274 
                 273 
                 275 
                 272 
                 284 
                 283 
                 285 
                 282 
               
               
                   
               
             
          
         
       
     
         [0108]    And, in another example, the maximum number of sequences can be predetermined to 3. The following tables 13 and 14 show this case. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
             
             
               
                 Group index 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 based on 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
                 12RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 2 
                 2 
                 3 
                 3 
                 2 
                 3 
                 4 
                 2 
                 4 
                 3 
                 5 
                 4 
                 5 
                 3 
               
               
                 2 
                 2 
                 3 
                 4 
                 5 
                 4 
                 6 
                 5 
                 7 
                 6 
                 8 
                 7 
                 8 
                 6 
                 9 
                 8 
                 10 
               
               
                 3 
                 3 
                 5 
                 6 
                 7 
                 6 
                 9 
                 8 
                 10 
                 11 
                 9 
                 11 
                 10 
                 12 
                 13 
                 14 
                 12 
               
               
                 4 
                 4 
                 6 
                 8 
                 9 
                 10 
                 11 
                 12 
                 14 
                 13 
                 15 
                 15 
                 14 
                 16 
                 18 
                 17 
                 19 
               
               
                 5 
                 5 
                 8 
                 10 
                 11 
                 12 
                 14 
                 15 
                 17 
                 18 
                 16 
                 18 
                 19 
                 17 
                 22 
                 23 
                 21 
               
               
                 6 
                 6 
                 9 
                 11 
                 14 
                 13 
                 17 
                 18 
                 21 
                 20 
                 22 
                 22 
                 21 
                 23 
                 27 
                 26 
                 28 
               
               
                 7 
                 7 
                 11 
                 13 
                 16 
                 17 
                 20 
                 21 
                 24 
                 25 
                 23 
                 26 
                 25 
                 27 
                 31 
                 32 
                 30 
               
               
                 8 
                 8 
                 12 
                 15 
                 18 
                 19 
                 23 
                 22 
                 28 
                 27 
                 29 
                 29 
                 30 
                 28 
                 36 
                 35 
                 37 
               
               
                 9 
                 9 
                 14 
                 17 
                 21 
                 20 
                 26 
                 25 
                 31 
                 32 
                 30 
                 33 
                 32 
                 34 
                 40 
                 41 
                 39 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 22 
                 29 
                 28 
                 35 
                 34 
                 36 
                 36 
                 37 
                 35 
                 45 
                 44 
                 46 
               
               
                 11 
                 11 
                 17 
                 21 
                 25 
                 26 
                 32 
                 31 
                 38 
                 37 
                 39 
                 40 
                 41 
                 39 
                 49 
                 50 
                 48 
               
               
                 12 
                 12 
                 18 
                 23 
                 27 
                 28 
                 34 
                 35 
                 41 
                 42 
                 40 
                 44 
                 43 
                 45 
                 54 
                 53 
                 55 
               
               
                 13 
                 13 
                 20 
                 25 
                 30 
                 29 
                 37 
                 38 
                 45 
                 44 
                 46 
                 47 
                 48 
                 46 
                 58 
                 59 
                 57 
               
               
                 14 
                 14 
                 21 
                 27 
                 32 
                 33 
                 40 
                 41 
                 48 
                 49 
                 47 
                 51 
                 52 
                 50 
                 63 
                 62 
                 64 
               
               
                 15 
                 15 
                 23 
                 29 
                 34 
                 35 
                 43 
                 44 
                 52 
                 51 
                 53 
                 55 
                 54 
                 56 
                 67 
                 68 
                 66 
               
               
                 16 
                 16 
                 24 
                 30 
                 37 
                 36 
                 46 
                 45 
                 55 
                 56 
                 54 
                 58 
                 59 
                 57 
                 72 
                 71 
                 73 
               
               
                 17 
                 17 
                 26 
                 32 
                 39 
                 38 
                 49 
                 48 
                 59 
                 58 
                 60 
                 62 
                 61 
                 63 
                 76 
                 77 
                 75 
               
               
                 18 
                 18 
                 27 
                 34 
                 41 
                 42 
                 52 
                 51 
                 62 
                 63 
                 61 
                 66 
                 65 
                 67 
                 81 
                 80 
                 82 
               
               
                 19 
                 19 
                 29 
                 36 
                 44 
                 43 
                 55 
                 54 
                 66 
                 65 
                 67 
                 69 
                 70 
                 68 
                 85 
                 86 
                 84 
               
               
                 20 
                 20 
                 30 
                 38 
                 46 
                 45 
                 57 
                 58 
                 69 
                 70 
                 68 
                 73 
                 72 
                 74 
                 90 
                 89 
                 91 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 49 
                 60 
                 61 
                 72 
                 73 
                 71 
                 77 
                 76 
                 78 
                 94 
                 95 
                 93 
               
               
                 22 
                 22 
                 33 
                 42 
                 50 
                 51 
                 63 
                 64 
                 76 
                 75 
                 77 
                 80 
                 81 
                 79 
                 99 
                 98 
                 100 
               
               
                 23 
                 23 
                 35 
                 44 
                 53 
                 52 
                 66 
                 67 
                 79 
                 80 
                 78 
                 84 
                 83 
                 85 
                 103 
                 104 
                 102 
               
               
                 24 
                 24 
                 36 
                 46 
                 55 
                 54 
                 69 
                 68 
                 83 
                 82 
                 84 
                 87 
                 88 
                 86 
                 108 
                 107 
                 109 
               
               
                 25 
                 25 
                 38 
                 48 
                 57 
                 58 
                 72 
                 71 
                 86 
                 87 
                 85 
                 91 
                 92 
                 90 
                 112 
                 113 
                 111 
               
               
                 26 
                 26 
                 39 
                 49 
                 60 
                 59 
                 75 
                 74 
                 90 
                 89 
                 91 
                 95 
                 94 
                 96 
                 117 
                 116 
                 118 
               
               
                 27 
                 27 
                 41 
                 51 
                 62 
                 61 
                 78 
                 77 
                 93 
                 94 
                 92 
                 98 
                 99 
                 97 
                 121 
                 122 
                 120 
               
               
                 28 
                 28 
                 42 
                 53 
                 64 
                 65 
                 80 
                 81 
                 97 
                 96 
                 98 
                 102 
                 103 
                 101 
                 126 
                 125 
                 127 
               
               
                 29 
                 29 
                 44 
                 55 
                 66 
                 67 
                 83 
                 84 
                 100 
                 101 
                 99 
                 106 
                 105 
                 107 
                 130 
                 131 
                 129 
               
               
                 30 
                 30 
                 45 
                 57 
                 69 
                 68 
                 86 
                 87 
                 104 
                 103 
                 105 
                 109 
                 110 
                 108 
                 135 
                 134 
                 136 
               
               
                   
               
             
          
           
               
                   
                 Group index 
                   
                   
                   
               
               
                   
                 based on 3RBs 
                 15RB 
                 16RB 
                 18RB 
               
               
                   
               
             
          
           
               
                   
                 1 
                 6 
                 5 
                 7 
                 6 
                 7 
                 5 
                 7 
                 6 
                 8 
               
               
                   
                 2 
                 12 
                 11 
                 13 
                 12 
                 13 
                 11 
                 14 
                 13 
                 15 
               
               
                   
                 3 
                 17 
                 18 
                 16 
                 18 
                 19 
                 17 
                 20 
                 21 
                 19 
               
               
                   
                 4 
                 23 
                 24 
                 22 
                 25 
                 24 
                 26 
                 27 
                 28 
                 26 
               
               
                   
                 5 
                 29 
                 28 
                 30 
                 31 
                 30 
                 32 
                 34 
                 35 
                 33 
               
               
                   
                 6 
                 35 
                 34 
                 36 
                 37 
                 36 
                 38 
                 41 
                 40 
                 42 
               
               
                   
                 7 
                 40 
                 41 
                 39 
                 43 
                 44 
                 42 
                 48 
                 47 
                 49 
               
               
                   
                 8 
                 46 
                 47 
                 45 
                 49 
                 50 
                 48 
                 54 
                 55 
                 53 
               
               
                   
                 9 
                 52 
                 51 
                 53 
                 55 
                 56 
                 54 
                 61 
                 62 
                 60 
               
               
                   
                 10 
                 58 
                 57 
                 59 
                 62 
                 61 
                 63 
                 68 
                 69 
                 67 
               
               
                   
                 11 
                 64 
                 63 
                 65 
                 68 
                 67 
                 69 
                 75 
                 74 
                 76 
               
               
                   
                 12 
                 69 
                 70 
                 68 
                 74 
                 73 
                 75 
                 82 
                 81 
                 83 
               
               
                   
                 13 
                 75 
                 76 
                 74 
                 80 
                 81 
                 79 
                 88 
                 89 
                 87 
               
               
                   
                 14 
                 81 
                 80 
                 82 
                 86 
                 87 
                 85 
                 95 
                 96 
                 94 
               
               
                   
                 15 
                 87 
                 86 
                 88 
                 92 
                 93 
                 91 
                 102 
                 103 
                 101 
               
               
                   
                 16 
                 92 
                 93 
                 91 
                 99 
                 98 
                 100 
                 109 
                 108 
                 110 
               
               
                   
                 17 
                 98 
                 99 
                 97 
                 105 
                 104 
                 106 
                 116 
                 115 
                 117 
               
               
                   
                 18 
                 104 
                 103 
                 105 
                 111 
                 110 
                 112 
                 123 
                 122 
                 124 
               
               
                   
                 19 
                 110 
                 109 
                 111 
                 117 
                 118 
                 116 
                 129 
                 130 
                 128 
               
               
                   
                 20 
                 115 
                 116 
                 114 
                 123 
                 124 
                 122 
                 136 
                 137 
                 135 
               
               
                   
                 21 
                 121 
                 122 
                 120 
                 129 
                 130 
                 128 
                 143 
                 142 
                 144 
               
               
                   
                 22 
                 127 
                 128 
                 126 
                 136 
                 135 
                 137 
                 150 
                 149 
                 151 
               
               
                   
                 23 
                 133 
                 132 
                 134 
                 142 
                 141 
                 143 
                 157 
                 156 
                 158 
               
               
                   
                 24 
                 139 
                 138 
                 140 
                 148 
                 147 
                 149 
                 163 
                 164 
                 162 
               
               
                   
                 25 
                 144 
                 145 
                 143 
                 154 
                 155 
                 153 
                 170 
                 171 
                 169 
               
               
                   
                 26 
                 150 
                 151 
                 149 
                 160 
                 161 
                 159 
                 177 
                 176 
                 178 
               
               
                   
                 27 
                 156 
                 155 
                 157 
                 166 
                 167 
                 165 
                 184 
                 183 
                 185 
               
               
                   
                 28 
                 162 
                 161 
                 163 
                 173 
                 172 
                 174 
                 191 
                 190 
                 192 
               
               
                   
                 29 
                 167 
                 168 
                 166 
                 179 
                 178 
                 180 
                 197 
                 198 
                 196 
               
               
                   
                 30 
                 173 
                 174 
                 172 
                 185 
                 184 
                 186 
                 204 
                 205 
                 203 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 Group index 
                   
                   
                   
               
               
                 based on 3RBs 
                 20RB 
                 24RB 
                 25RBs 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 8 
                 7 
                 9 
                 9 
                 10 
                 8 
                 9 
                 10 
                 8 
               
               
                 2 
                 15 
                 16 
                 14 
                 18 
                 19 
                 17 
                 19 
                 18 
                 20 
               
               
                 3 
                 23 
                 24 
                 22 
                 27 
                 28 
                 26 
                 28 
                 29 
                 27 
               
               
                 4 
                 31 
                 30 
                 32 
                 37 
                 36 
                 38 
                 38 
                 37 
                 39 
               
               
                 5 
                 39 
                 38 
                 40 
                 46 
                 45 
                 47 
                 47 
                 48 
                 46 
               
               
                 6 
                 46 
                 47 
                 45 
                 55 
                 54 
                 56 
                 57 
                 56 
                 58 
               
               
                 7 
                 54 
                 53 
                 55 
                 64 
                 63 
                 65 
                 66 
                 67 
                 65 
               
               
                 8 
                 62 
                 61 
                 63 
                 73 
                 74 
                 72 
                 76 
                 75 
                 77 
               
               
                 9 
                 69 
                 70 
                 68 
                 82 
                 83 
                 81 
                 85 
                 86 
                 84 
               
               
                 10 
                 77 
                 78 
                 76 
                 91 
                 92 
                 90 
                 95 
                 94 
                 96 
               
               
                 11 
                 85 
                 84 
                 86 
                 100 
                 101 
                 99 
                 104 
                 103 
                 105 
               
               
                 12 
                 93 
                 92 
                 94 
                 110 
                 109 
                 111 
                 113 
                 114 
                 112 
               
               
                 13 
                 100 
                 101 
                 99 
                 119 
                 118 
                 120 
                 123 
                 122 
                 124 
               
               
                 14 
                 108 
                 107 
                 109 
                 128 
                 127 
                 129 
                 132 
                 133 
                 131 
               
               
                 15 
                 116 
                 115 
                 117 
                 137 
                 136 
                 138 
                 142 
                 141 
                 143 
               
               
                 16 
                 123 
                 124 
                 122 
                 146 
                 147 
                 145 
                 151 
                 152 
                 150 
               
               
                 17 
                 131 
                 132 
                 130 
                 155 
                 156 
                 154 
                 161 
                 160 
                 162 
               
               
                 18 
                 139 
                 138 
                 140 
                 164 
                 165 
                 163 
                 170 
                 171 
                 169 
               
               
                 19 
                 146 
                 147 
                 145 
                 173 
                 174 
                 172 
                 180 
                 179 
                 181 
               
               
                 20 
                 154 
                 155 
                 153 
                 183 
                 182 
                 184 
                 189 
                 190 
                 188 
               
               
                 21 
                 162 
                 161 
                 163 
                 192 
                 191 
                 193 
                 198 
                 199 
                 197 
               
               
                 22 
                 170 
                 169 
                 171 
                 201 
                 200 
                 202 
                 208 
                 207 
                 209 
               
               
                 23 
                 177 
                 178 
                 176 
                 210 
                 209 
                 211 
                 217 
                 218 
                 216 
               
               
                 24 
                 185 
                 186 
                 184 
                 219 
                 220 
                 218 
                 227 
                 226 
                 228 
               
               
                 25 
                 193 
                 192 
                 194 
                 228 
                 229 
                 227 
                 236 
                 237 
                 235 
               
               
                 26 
                 200 
                 201 
                 199 
                 237 
                 238 
                 236 
                 246 
                 245 
                 247 
               
               
                 27 
                 208 
                 209 
                 207 
                 246 
                 247 
                 245 
                 255 
                 256 
                 254 
               
               
                 28 
                 216 
                 215 
                 217 
                 256 
                 255 
                 257 
                 265 
                 264 
                 266 
               
               
                 29 
                 224 
                 223 
                 225 
                 265 
                 264 
                 266 
                 274 
                 275 
                 273 
               
               
                 30 
                 231 
                 232 
                 230 
                 274 
                 273 
                 275 
                 284 
                 283 
                 285 
               
               
                   
               
             
          
         
       
     
         [0109]    And, in another example, the maximum number of sequences can be predetermined to 2. The following tables 15 and 16 show this case. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 15 
               
               
                   
               
               
                 Group index 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 based on 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
                 12RB 
                 15RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 2 
                 2 
                 3 
                 3 
                 2 
                 3 
                 4 
                 4 
                 3 
                 4 
                 5 
                 6 
                 5 
               
               
                 2 
                 2 
                 3 
                 4 
                 5 
                 4 
                 6 
                 5 
                 7 
                 6 
                 7 
                 8 
                 9 
                 8 
                 12 
                 11 
               
               
                 3 
                 3 
                 5 
                 6 
                 7 
                 6 
                 9 
                 8 
                 10 
                 11 
                 11 
                 10 
                 13 
                 14 
                 17 
                 18 
               
               
                 4 
                 4 
                 6 
                 8 
                 9 
                 10 
                 11 
                 12 
                 14 
                 13 
                 15 
                 14 
                 18 
                 17 
                 23 
                 24 
               
               
                 5 
                 5 
                 8 
                 10 
                 11 
                 12 
                 14 
                 15 
                 17 
                 18 
                 18 
                 19 
                 22 
                 23 
                 29 
                 28 
               
               
                 6 
                 6 
                 9 
                 11 
                 14 
                 13 
                 17 
                 18 
                 21 
                 20 
                 22 
                 21 
                 27 
                 26 
                 35 
                 34 
               
               
                 7 
                 7 
                 11 
                 13 
                 16 
                 17 
                 20 
                 21 
                 24 
                 25 
                 26 
                 25 
                 31 
                 32 
                 40 
                 41 
               
               
                 8 
                 8 
                 12 
                 15 
                 18 
                 19 
                 23 
                 22 
                 28 
                 27 
                 29 
                 30 
                 36 
                 35 
                 46 
                 47 
               
               
                 9 
                 9 
                 14 
                 17 
                 21 
                 20 
                 26 
                 25 
                 31 
                 32 
                 33 
                 32 
                 40 
                 41 
                 52 
                 51 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 22 
                 29 
                 28 
                 35 
                 34 
                 36 
                 37 
                 45 
                 44 
                 58 
                 57 
               
               
                 11 
                 11 
                 17 
                 21 
                 25 
                 26 
                 32 
                 31 
                 38 
                 37 
                 40 
                 41 
                 49 
                 50 
                 64 
                 63 
               
               
                 12 
                 12 
                 18 
                 23 
                 27 
                 28 
                 34 
                 35 
                 41 
                 42 
                 44 
                 43 
                 54 
                 53 
                 69 
                 70 
               
               
                 13 
                 13 
                 20 
                 25 
                 30 
                 29 
                 37 
                 38 
                 45 
                 44 
                 47 
                 48 
                 58 
                 59 
                 75 
                 76 
               
               
                 14 
                 14 
                 21 
                 27 
                 32 
                 33 
                 40 
                 41 
                 48 
                 49 
                 51 
                 52 
                 63 
                 62 
                 81 
                 80 
               
               
                 15 
                 15 
                 23 
                 29 
                 34 
                 35 
                 43 
                 44 
                 52 
                 51 
                 55 
                 54 
                 67 
                 68 
                 87 
                 86 
               
               
                 16 
                 16 
                 24 
                 30 
                 37 
                 36 
                 46 
                 45 
                 55 
                 56 
                 58 
                 49 
                 72 
                 71 
                 92 
                 93 
               
               
                 17 
                 17 
                 26 
                 32 
                 39 
                 38 
                 49 
                 48 
                 59 
                 58 
                 62 
                 61 
                 76 
                 77 
                 98 
                 99 
               
               
                 18 
                 18 
                 27 
                 34 
                 41 
                 42 
                 52 
                 51 
                 62 
                 63 
                 66 
                 65 
                 81 
                 80 
                 104 
                 103 
               
               
                 19 
                 19 
                 29 
                 36 
                 44 
                 43 
                 55 
                 54 
                 66 
                 65 
                 69 
                 70 
                 85 
                 86 
                 110 
                 109 
               
               
                 20 
                 20 
                 30 
                 38 
                 46 
                 45 
                 57 
                 58 
                 69 
                 70 
                 73 
                 72 
                 90 
                 89 
                 115 
                 116 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 49 
                 60 
                 61 
                 72 
                 73 
                 77 
                 76 
                 94 
                 95 
                 121 
                 122 
               
               
                 22 
                 22 
                 33 
                 42 
                 50 
                 51 
                 63 
                 64 
                 76 
                 75 
                 80 
                 81 
                 99 
                 98 
                 127 
                 128 
               
               
                 23 
                 23 
                 35 
                 44 
                 53 
                 52 
                 66 
                 67 
                 79 
                 80 
                 84 
                 83 
                 103 
                 104 
                 133 
                 132 
               
               
                 24 
                 24 
                 36 
                 46 
                 55 
                 54 
                 69 
                 68 
                 83 
                 82 
                 87 
                 88 
                 108 
                 107 
                 139 
                 138 
               
               
                 25 
                 25 
                 38 
                 48 
                 57 
                 58 
                 72 
                 71 
                 86 
                 87 
                 91 
                 92 
                 112 
                 113 
                 144 
                 145 
               
               
                 26 
                 26 
                 39 
                 49 
                 60 
                 59 
                 75 
                 74 
                 90 
                 89 
                 95 
                 94 
                 117 
                 116 
                 150 
                 151 
               
               
                 27 
                 27 
                 41 
                 51 
                 62 
                 61 
                 78 
                 77 
                 93 
                 94 
                 98 
                 99 
                 121 
                 122 
                 156 
                 155 
               
               
                 28 
                 28 
                 42 
                 53 
                 64 
                 65 
                 80 
                 81 
                 97 
                 96 
                 102 
                 103 
                 126 
                 125 
                 162 
                 161 
               
               
                 29 
                 29 
                 44 
                 55 
                 66 
                 67 
                 83 
                 84 
                 100 
                 101 
                 106 
                 105 
                 130 
                 131 
                 167 
                 168 
               
               
                 30 
                 30 
                 45 
                 57 
                 69 
                 68 
                 86 
                 87 
                 104 
                 103 
                 109 
                 110 
                 135 
                 134 
                 173 
                 174 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 16 
               
               
                   
               
               
                 Gr. 
                   
                   
                   
                   
                   
               
               
                 Idx 
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 16RB 
                 18RB 
                 20RB 
                 24RB 
                 25RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 6 
                 7 
                 7 
                 6 
                 8 
                 7 
                 9 
                 10 
                 9 
                 10 
               
               
                 2 
                 12 
                 13 
                 14 
                 13 
                 15 
                 16 
                 18 
                 19 
                 19 
                 18 
               
               
                 3 
                 18 
                 19 
                 20 
                 21 
                 23 
                 24 
                 27 
                 28 
                 28 
                 29 
               
               
                 4 
                 25 
                 24 
                 27 
                 28 
                 31 
                 30 
                 37 
                 36 
                 38 
                 37 
               
               
                 5 
                 31 
                 30 
                 34 
                 35 
                 39 
                 38 
                 46 
                 45 
                 47 
                 48 
               
               
                 6 
                 37 
                 36 
                 41 
                 40 
                 46 
                 47 
                 55 
                 54 
                 57 
                 56 
               
               
                 7 
                 43 
                 44 
                 48 
                 47 
                 54 
                 53 
                 64 
                 63 
                 66 
                 67 
               
               
                 8 
                 49 
                 50 
                 54 
                 55 
                 62 
                 61 
                 73 
                 74 
                 76 
                 75 
               
               
                 9 
                 55 
                 56 
                 61 
                 62 
                 69 
                 70 
                 82 
                 83 
                 85 
                 86 
               
               
                 10 
                 62 
                 61 
                 68 
                 69 
                 77 
                 78 
                 91 
                 92 
                 95 
                 94 
               
               
                 11 
                 68 
                 67 
                 75 
                 74 
                 85 
                 84 
                 100 
                 101 
                 104 
                 103 
               
               
                 12 
                 74 
                 73 
                 82 
                 81 
                 93 
                 92 
                 110 
                 109 
                 113 
                 114 
               
               
                 13 
                 80 
                 81 
                 88 
                 89 
                 100 
                 101 
                 119 
                 118 
                 123 
                 122 
               
               
                 14 
                 86 
                 87 
                 95 
                 96 
                 108 
                 107 
                 128 
                 127 
                 132 
                 133 
               
               
                 15 
                 92 
                 93 
                 102 
                 103 
                 116 
                 115 
                 137 
                 136 
                 142 
                 141 
               
               
                 16 
                 99 
                 98 
                 109 
                 108 
                 123 
                 124 
                 146 
                 147 
                 151 
                 152 
               
               
                 17 
                 105 
                 104 
                 116 
                 115 
                 131 
                 132 
                 155 
                 156 
                 161 
                 160 
               
               
                 18 
                 111 
                 110 
                 123 
                 122 
                 139 
                 138 
                 164 
                 165 
                 170 
                 171 
               
               
                 19 
                 117 
                 118 
                 129 
                 130 
                 146 
                 147 
                 173 
                 174 
                 180 
                 179 
               
               
                 20 
                 123 
                 124 
                 136 
                 137 
                 154 
                 155 
                 183 
                 182 
                 189 
                 190 
               
               
                 21 
                 129 
                 130 
                 143 
                 142 
                 162 
                 161 
                 192 
                 191 
                 198 
                 199 
               
               
                 22 
                 136 
                 135 
                 150 
                 149 
                 170 
                 169 
                 201 
                 200 
                 208 
                 207 
               
               
                 23 
                 142 
                 141 
                 157 
                 156 
                 177 
                 178 
                 210 
                 209 
                 217 
                 218 
               
               
                 24 
                 148 
                 147 
                 163 
                 164 
                 185 
                 186 
                 219 
                 220 
                 227 
                 226 
               
               
                 25 
                 154 
                 155 
                 170 
                 171 
                 193 
                 192 
                 228 
                 229 
                 236 
                 237 
               
               
                 26 
                 160 
                 161 
                 177 
                 176 
                 200 
                 201 
                 237 
                 238 
                 246 
                 245 
               
               
                 27 
                 166 
                 167 
                 184 
                 183 
                 208 
                 209 
                 246 
                 247 
                 255 
                 256 
               
               
                 28 
                 173 
                 172 
                 191 
                 190 
                 216 
                 215 
                 256 
                 255 
                 265 
                 264 
               
               
                 29 
                 179 
                 178 
                 197 
                 198 
                 224 
                 223 
                 265 
                 264 
                 274 
                 275 
               
               
                 30 
                 185 
                 184 
                 204 
                 205 
                 231 
                 232 
                 274 
                 273 
                 284 
                 283 
               
               
                   
               
             
          
         
       
     
         [0110]    And, in another example, the maximum number of sequences can be predetermined to 1. The following table 17 shows this case. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 17 
               
               
                   
               
               
                 Gr. 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Idx 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
                 12RB 
                 15RB 
                 16RB 
                 18RB 
                 20RB 
                 24RB 
                 25RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 2 
                 2 
                 3 
                 3 
                 4 
                 4 
                 6 
                 6 
                 7 
                 8 
                 9 
                 9 
               
               
                 2 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 7 
                 9 
                 12 
                 12 
                 14 
                 15 
                 18 
                 19 
               
               
                 3 
                 3 
                 5 
                 6 
                 7 
                 9 
                 10 
                 11 
                 13 
                 17 
                 18 
                 20 
                 23 
                 27 
                 28 
               
               
                 4 
                 4 
                 6 
                 8 
                 9 
                 11 
                 14 
                 15 
                 18 
                 23 
                 25 
                 27 
                 31 
                 37 
                 38 
               
               
                 5 
                 5 
                 8 
                 10 
                 11 
                 14 
                 17 
                 18 
                 22 
                 29 
                 31 
                 34 
                 39 
                 46 
                 47 
               
               
                 6 
                 6 
                 9 
                 11 
                 14 
                 17 
                 21 
                 22 
                 27 
                 35 
                 37 
                 41 
                 46 
                 55 
                 57 
               
               
                 7 
                 7 
                 11 
                 13 
                 16 
                 20 
                 24 
                 26 
                 31 
                 40 
                 43 
                 48 
                 54 
                 64 
                 66 
               
               
                 8 
                 8 
                 12 
                 15 
                 18 
                 23 
                 28 
                 29 
                 36 
                 46 
                 49 
                 54 
                 62 
                 73 
                 76 
               
               
                 9 
                 9 
                 14 
                 17 
                 21 
                 26 
                 31 
                 33 
                 40 
                 52 
                 55 
                 61 
                 69 
                 82 
                 85 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 29 
                 35 
                 36 
                 45 
                 58 
                 62 
                 68 
                 77 
                 91 
                 95 
               
               
                 11 
                 11 
                 17 
                 21 
                 25 
                 32 
                 38 
                 40 
                 49 
                 64 
                 68 
                 75 
                 85 
                 100 
                 104 
               
               
                 12 
                 12 
                 18 
                 23 
                 27 
                 34 
                 41 
                 44 
                 54 
                 69 
                 74 
                 82 
                 93 
                 110 
                 113 
               
               
                 13 
                 13 
                 20 
                 25 
                 30 
                 37 
                 45 
                 47 
                 58 
                 75 
                 80 
                 88 
                 100 
                 119 
                 123 
               
               
                 14 
                 14 
                 21 
                 27 
                 32 
                 40 
                 48 
                 51 
                 63 
                 81 
                 86 
                 95 
                 108 
                 128 
                 132 
               
               
                 15 
                 15 
                 23 
                 29 
                 34 
                 43 
                 52 
                 55 
                 67 
                 87 
                 92 
                 102 
                 116 
                 137 
                 142 
               
               
                 16 
                 16 
                 24 
                 30 
                 37 
                 46 
                 55 
                 58 
                 72 
                 92 
                 99 
                 109 
                 123 
                 146 
                 151 
               
               
                 17 
                 17 
                 26 
                 32 
                 39 
                 49 
                 59 
                 62 
                 76 
                 98 
                 105 
                 116 
                 131 
                 155 
                 161 
               
               
                 18 
                 18 
                 27 
                 34 
                 41 
                 52 
                 62 
                 66 
                 81 
                 104 
                 111 
                 123 
                 139 
                 164 
                 170 
               
               
                 19 
                 19 
                 29 
                 36 
                 44 
                 55 
                 66 
                 69 
                 85 
                 110 
                 117 
                 129 
                 146 
                 173 
                 180 
               
               
                 20 
                 20 
                 30 
                 38 
                 46 
                 57 
                 69 
                 73 
                 90 
                 115 
                 123 
                 136 
                 154 
                 183 
                 189 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 60 
                 72 
                 77 
                 94 
                 121 
                 129 
                 143 
                 162 
                 192 
                 198 
               
               
                 22 
                 22 
                 33 
                 42 
                 50 
                 63 
                 76 
                 80 
                 99 
                 127 
                 136 
                 150 
                 170 
                 201 
                 208 
               
               
                 23 
                 23 
                 35 
                 44 
                 53 
                 66 
                 79 
                 84 
                 103 
                 133 
                 142 
                 157 
                 177 
                 210 
                 217 
               
               
                 24 
                 24 
                 36 
                 46 
                 55 
                 69 
                 83 
                 87 
                 108 
                 139 
                 148 
                 163 
                 185 
                 219 
                 227 
               
               
                 25 
                 25 
                 38 
                 48 
                 57 
                 72 
                 86 
                 91 
                 112 
                 144 
                 154 
                 170 
                 193 
                 228 
                 236 
               
               
                 26 
                 26 
                 39 
                 49 
                 60 
                 75 
                 90 
                 95 
                 117 
                 150 
                 160 
                 177 
                 200 
                 237 
                 246 
               
               
                 27 
                 27 
                 41 
                 51 
                 62 
                 78 
                 93 
                 98 
                 121 
                 156 
                 166 
                 184 
                 208 
                 246 
                 255 
               
               
                 28 
                 28 
                 42 
                 53 
                 64 
                 80 
                 97 
                 102 
                 126 
                 162 
                 173 
                 191 
                 216 
                 256 
                 265 
               
               
                 29 
                 29 
                 44 
                 55 
                 66 
                 83 
                 100 
                 106 
                 130 
                 167 
                 179 
                 197 
                 224 
                 265 
                 274 
               
               
                 30 
                 30 
                 45 
                 57 
                 69 
                 86 
                 104 
                 109 
                 135 
                 173 
                 185 
                 204 
                 231 
                 274 
                 284 
               
               
                   
               
             
          
         
       
     
         [0111]    Considering the complexity of configuration and the flexibility for supporting UE(s) to use variable length reference signal sequence, one embodiment of this invention proposes to perform grouping such that each of the groups contains one base sequence of each length corresponding to 1 to 5 RB length, and two base sequences of each length corresponding to 6 RB or more length. This corresponds to the tables 15 and 16. 
         [0112]    Here, base sequence means the ZC sequence indicated by the root index, and is used for applying the cyclic shift corresponding to various cyclic shift values. And, the base sequence with cyclic shift can be used as a reference signal sequence. 
         [0113]    The above tables 1˜17 is the case when the root index(es) is selected by using the term of (s 1 /N 1 −s z /N 2 ). But in another embodiment of this invention, the root index(es) can be selected by actual cross correlation value calculation. The following tables 18˜20 correspond to the tables 6˜8, but the root indexes are selected by actual cross correlation value calculation. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 18 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 25 
                 2 
                 20 
                 2 
                 3 
                 25 
                 57 
                 4 
                 75 
                 60 
                 79 
                 4 
               
               
                 2 
                 2 
                 3 
                 4 
                 40 
                 33 
                 65 
                 28 
                 7 
                 71 
                 96 
                 64 
                 45 
                 75 
               
               
                 3 
                 3 
                 14 
                 6 
                 7 
                 21 
                 53 
                 9 
                 46 
                 10 
                 37 
                 11 
                 39 
                 86 
               
               
                 4 
                 4 
                 6 
                 47 
                 9 
                 66 
                 56 
                 41 
                 14 
                 85 
                 78 
                 15 
                 71 
                 14 
               
               
                 5 
                 5 
                 39 
                 39 
                 47 
                 54 
                 44 
                 50 
                 71 
                 44 
                 60 
                 56 
                 75 
                 103 
               
               
                 6 
                 6 
                 9 
                 31 
                 61 
                 14 
                 17 
                 84 
                 21 
                 92 
                 85 
                 97 
                 50 
                 67 
               
               
                 7 
                 7 
                 42 
                 33 
                 16 
                 28 
                 20 
                 87 
                 24 
                 51 
                 60 
                 82 
                 63 
                 26 
               
               
                 8 
                 8 
                 12 
                 30 
                 42 
                 54 
                 23 
                 5 
                 28 
                 99 
                 49 
                 67 
                 86 
                 1 
               
               
                 9 
                 9 
                 45 
                 17 
                 68 
                 21 
                 48 
                 85 
                 31 
                 74 
                 58 
                 61 
                 89 
                 78 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 5 
                 73 
                 29 
                 106 
                 70 
                 34 
                 93 
                 112 
                 36 
               
               
                 11 
                 11 
                 1 
                 21 
                 11 
                 25 
                 32 
                 2 
                 38 
                 102 
                 11 
                 40 
                 78 
                 12 
               
               
                 12 
                 12 
                 37 
                 23 
                 51 
                 63 
                 79 
                 64 
                 96 
                 77 
                 41 
                 72 
                 44 
                 100 
               
               
                 13 
                 13 
                 4 
                 5 
                 6 
                 30 
                 67 
                 37 
                 45 
                 9 
                 18 
                 104 
                 47 
                 85 
               
               
                 14 
                 14 
                 21 
                 7 
                 32 
                 22 
                 40 
                 58 
                 102 
                 84 
                 48 
                 51 
                 6 
                 23 
               
               
                 15 
                 15 
                 23 
                 58 
                 58 
                 34 
                 43 
                 61 
                 105 
                 16 
                 25 
                 17 
                 111 
                 83 
               
               
                 16 
                 16 
                 24 
                 1 
                 13 
                 65 
                 46 
                 28 
                 91 
                 2 
                 82 
                 96 
                 2 
                 30 
               
               
                 17 
                 17 
                 26 
                 52 
                 39 
                 49 
                 31 
                 49 
                 23 
                 59 
                 16 
                 62 
                 107 
                 90 
               
               
                 18 
                 18 
                 43 
                 54 
                 65 
                 41 
                 22 
                 52 
                 62 
                 98 
                 89 
                 9 
                 66 
                 28 
               
               
                 19 
                 19 
                 29 
                 36 
                 8 
                 20 
                 10 
                 25 
                 30 
                 12 
                 87 
                 41 
                 24 
                 70 
               
               
                 20 
                 20 
                 46 
                 38 
                 46 
                 60 
                 87 
                 57 
                 69 
                 5 
                 96 
                 73 
                 35 
                 101 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 66 
                 16 
                 60 
                 1 
                 37 
                 73 
                 20 
                 1 
                 39 
               
               
                 22 
                 22 
                 2 
                 42 
                 3 
                 50 
                 41 
                 78 
                 76 
                 49 
                 33 
                 52 
                 24 
                 35 
               
               
                 23 
                 23 
                 35 
                 29 
                 29 
                 17 
                 66 
                 55 
                 79 
                 8 
                 58 
                 46 
                 27 
                 112 
               
               
                 24 
                 24 
                 5 
                 26 
                 55 
                 43 
                 69 
                 2 
                 83 
                 56 
                 47 
                 31 
                 12 
                 88 
               
               
                 25 
                 25 
                 38 
                 28 
                 10 
                 57 
                 72 
                 27 
                 15 
                 65 
                 86 
                 63 
                 46 
                 16 
               
               
                 26 
                 26 
                 8 
                 20 
                 24 
                 17 
                 45 
                 75 
                 63 
                 54 
                 90 
                 95 
                 57 
                 38 
               
               
                 27 
                 27 
                 41 
                 22 
                 62 
                 44 
                 33 
                 48 
                 93 
                 22 
                 29 
                 23 
                 98 
                 42 
               
               
                 28 
                 28 
                 33 
                 53 
                 64 
                 50 
                 36 
                 80 
                 61 
                 97 
                 70 
                 102 
                 57 
                 74 
               
               
                 29 
                 29 
                 44 
                 8 
                 31 
                 38 
                 24 
                 39 
                 100 
                 36 
                 11 
                 49 
                 68 
                 106 
               
               
                 30 
                 30 
                 22 
                 55 
                 69 
                 51 
                 86 
                 64 
                 50 
                 103 
                 18 
                 34 
                 109 
                 81 
               
               
                   
               
             
          
           
               
                   
                 Gr. Idx 
                   
                   
               
               
                   
                 3RBs 
                 12RB 
                 15RB 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 74 
                 51 
                 4 
                 5 
                 6 
                 95 
                 140 
                 125 
                 5 
               
               
                   
                 2 
                 9 
                 120 
                 44 
                 8 
                 101 
                 71 
                 131 
                 12 
                 11 
               
               
                   
                 3 
                 83 
                 13 
                 14 
                 48 
                 17 
                 107 
                 77 
                 18 
                 62 
               
               
                   
                 4 
                 18 
                 122 
                 87 
                 129 
                 23 
                 83 
                 113 
                 68 
                 24 
               
               
                   
                 5 
                 92 
                 23 
                 115 
                 78 
                 29 
                 118 
                 148 
                 28 
                 163 
               
               
                   
                 6 
                 27 
                 96 
                 131 
                 73 
                 35 
                 154 
                 124 
                 34 
                 94 
               
               
                   
                 7 
                 101 
                 124 
                 32 
                 66 
                 40 
                 130 
                 160 
                 41 
                 100 
               
               
                   
                 8 
                 36 
                 105 
                 8 
                 59 
                 46 
                 136 
                 106 
                 47 
                 91 
               
               
                   
                 9 
                 133 
                 110 
                 41 
                 75 
                 52 
                 141 
                 171 
                 142 
                 7 
               
               
                   
                 10 
                 45 
                 114 
                 91 
                 17 
                 58 
                 147 
                 57 
                 177 
                 13 
               
               
                   
                 11 
                 119 
                 3 
                 50 
                 77 
                 64 
                 153 
                 4 
                 63 
                 19 
               
               
                   
                 12 
                 54 
                 100 
                 123 
                 26 
                 69 
                 159 
                 129 
                 114 
                 10 
               
               
                   
                 13 
                 12 
                 58 
                 128 
                 114 
                 75 
                 165 
                 153 
                 120 
                 76 
               
               
                   
                 14 
                 63 
                 132 
                 7 
                 35 
                 81 
                 21 
                 170 
                 36 
                 80 
               
               
                   
                 15 
                 67 
                 137 
                 21 
                 68 
                 86 
                 27 
                 176 
                 146 
                 42 
               
               
                   
                 16 
                 2 
                 118 
                 71 
                 16 
                 93 
                 152 
                 3 
                 33 
                 137 
               
               
                   
                 17 
                 7 
                 76 
                 77 
                 132 
                 158 
                 98 
                 9 
                 143 
                 134 
               
               
                   
                 18 
                 11 
                 127 
                 81 
                 25 
                 104 
                 14 
                 44 
                 59 
                 103 
               
               
                   
                 19 
                 85 
                 39 
                 16 
                 113 
                 20 
                 50 
                 110 
                 65 
                 169 
               
               
                   
                 20 
                 136 
                 20 
                 89 
                 43 
                 115 
                 26 
                 175 
                 116 
                 71 
               
               
                   
                 21 
                 94 
                 48 
                 25 
                 129 
                 121 
                 32 
                 122 
                 2 
                 166 
               
               
                   
                 22 
                 6 
                 64 
                 52 
                 99 
                 127 
                 38 
                 8 
                 172 
                 67 
               
               
                   
                 23 
                 103 
                 34 
                 131 
                 80 
                 133 
                 73 
                 132 
                 88 
                 43 
               
               
                   
                 24 
                 38 
                 15 
                 73 
                 108 
                 139 
                 49 
                 19 
                 138 
                 79 
               
               
                   
                 25 
                 112 
                 66 
                 43 
                 113 
                 144 
                 25 
                 55 
                 145 
                 85 
               
               
                   
                 26 
                 47 
                 116 
                 24 
                 61 
                 150 
                 61 
                 31 
                 151 
                 16 
               
               
                   
                 27 
                 121 
                 75 
                 52 
                 17 
                 156 
                 96 
                 155 
                 66 
                 111 
               
               
                   
                 28 
                 56 
                 79 
                 126 
                 125 
                 162 
                 72 
                 102 
                 42 
                 161 
               
               
                   
                 29 
                 130 
                 95 
                 19 
                 131 
                 78 
                 48 
                 108 
                 167 
                 168 
               
               
                   
                 30 
                 65 
                 135 
                 134 
                 100 
                 173 
                 54 
                 84 
                 39 
                 174 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 19 
               
               
                   
               
               
                 Gr. 
                   
                   
                   
               
               
                 Idx 
               
               
                 3RBs 
                 16RB 
                 18RB 
                 20RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 6 
                 102 
                 70 
                 54 
                 7 
                 159 
                 112 
                 7 
                 6 
                 165 
                 49 
                 147 
                 8 
                 8 
                 7 
                 167 
                 127 
                 87 
                 9 
                 187 
               
               
                 2 
                 76 
                 12 
                 108 
                 140 
                 60 
                 13 
                 119 
                 14 
                 84 
                 154 
                 98 
                 56 
                 13 
                 15 
                 135 
                 95 
                 175 
                 75 
                 16 
                 111 
               
               
                 3 
                 18 
                 114 
                 19 
                 82 
                 66 
                 146 
                 20 
                 126 
                 91 
                 161 
                 21 
                 73 
                 147 
                 23 
                 143 
                 103 
                 24 
                 142 
                 22 
                 71 
               
               
                 4 
                 25 
                 152 
                 120 
                 24 
                 88 
                 168 
                 133 
                 28 
                 168 
                 98 
                 196 
                 80 
                 154 
                 31 
                 150 
                 190 
                 30 
                 32 
                 210 
                 111 
               
               
                 5 
                 30 
                 158 
                 174 
                 69 
                 31 
                 107 
                 34 
                 175 
                 139 
                 33 
                 35 
                 87 
                 203 
                 39 
                 38 
                 158 
                 118 
                 218 
                 198 
                 98 
               
               
                 6 
                 37 
                 132 
                 101 
                 133 
                 180 
                 38 
                 41 
                 146 
                 40 
                 199 
                 182 
                 181 
                 83 
                 46 
                 126 
                 47 
                 45 
                 106 
                 94 
                 206 
               
               
                 7 
                 43 
                 139 
                 107 
                 91 
                 44 
                 170 
                 48 
                 153 
                 118 
                 188 
                 206 
                 47 
                 174 
                 54 
                 174 
                 173 
                 134 
                 53 
                 55 
                 213 
               
               
                 8 
                 49 
                 113 
                 145 
                 50 
                 97 
                 177 
                 54 
                 195 
                 139 
                 181 
                 2 
                 55 
                 53 
                 62 
                 181 
                 221 
                 61 
                 2 
                 141 
                 63 
               
               
                 9 
                 151 
                 103 
                 56 
                 132 
                 183 
                 8 
                 61 
                 202 
                 62 
                 132 
                 114 
                 19 
                 167 
                 69 
                 189 
                 70 
                 149 
                 129 
                 229 
                 10 
               
               
                 10 
                 62 
                 157 
                 189 
                 61 
                 14 
                 125 
                 68 
                 174 
                 209 
                 173 
                 138 
                 121 
                 69 
                 77 
                 197 
                 157 
                 196 
                 76 
                 236 
                 137 
               
               
                 11 
                 68 
                 67 
                 163 
                 20 
                 106 
                 4 
                 75 
                 74 
                 76 
                 5 
                 181 
                 180 
                 159 
                 85 
                 204 
                 5 
                 84 
                 164 
                 25 
                 86 
               
               
                 12 
                 74 
                 169 
                 10 
                 138 
                 170 
                 75 
                 187 
                 152 
                 81 
                 82 
                 166 
                 29 
                 208 
                 92 
                 13 
                 172 
                 33 
                 152 
                 236 
                 212 
               
               
                 13 
                 80 
                 176 
                 81 
                 144 
                 79 
                 16 
                 194 
                 36 
                 141 
                 159 
                 18 
                 89 
                 173 
                 220 
                 180 
                 101 
                 21 
                 100 
                 160 
                 148 
               
               
                 14 
                 86 
                 150 
                 182 
                 87 
                 10 
                 48 
                 95 
                 201 
                 25 
                 96 
                 11 
                 166 
                 180 
                 108 
                 107 
                 109 
                 188 
                 228 
                 48 
                 168 
               
               
                 15 
                 188 
                 93 
                 29 
                 156 
                 92 
                 140 
                 102 
                 208 
                 32 
                 103 
                 172 
                 101 
                 207 
                 116 
                 36 
                 235 
                 115 
                 195 
                 56 
                 68 
               
               
                 16 
                 3 
                 98 
                 162 
                 35 
                 99 
                 51 
                 109 
                 3 
                 179 
                 56 
                 110 
                 39 
                 4 
                 123 
                 203 
                 4 
                 124 
                 44 
                 183 
                 171 
               
               
                 17 
                 105 
                 41 
                 9 
                 104 
                 181 
                 143 
                 116 
                 10 
                 186 
                 115 
                 200 
                 31 
                 45 
                 131 
                 132 
                 130 
                 51 
                 11 
                 191 
                 71 
               
               
                 18 
                 111 
                 47 
                 15 
                 110 
                 175 
                 149 
                 17 
                 175 
                 70 
                 52 
                 193 
                 122 
                 38 
                 19 
                 59 
                 138 
                 139 
                 218 
                 140 
                 79 
               
               
                 19 
                 117 
                 22 
                 181 
                 21 
                 116 
                 53 
                 24 
                 59 
                 130 
                 182 
                 129 
                 45 
                 3 
                 27 
                 147 
                 146 
                 226 
                 206 
                 87 
                 67 
               
               
                 20 
                 28 
                 123 
                 124 
                 171 
                 85 
                 187 
                 136 
                 31 
                 137 
                 135 
                 206 
                 52 
                 66 
                 35 
                 154 
                 234 
                 155 
                 214 
                 75 
                 153 
               
               
                 21 
                 129 
                 34 
                 2 
                 66 
                 130 
                 177 
                 143 
                 37 
                 2 
                 73 
                 142 
                 196 
                 185 
                 162 
                 42 
                 82 
                 43 
                 163 
                 3 
                 102 
               
               
                 22 
                 135 
                 136 
                 59 
                 8 
                 183 
                 21 
                 150 
                 9 
                 149 
                 44 
                 79 
                 97 
                 192 
                 170 
                 169 
                 50 
                 90 
                 110 
                 10 
                 74 
               
               
                 23 
                 142 
                 78 
                 46 
                 94 
                 141 
                 14 
                 16 
                 30 
                 209 
                 157 
                 72 
                 156 
                 158 
                 58 
                 177 
                 18 
                 178 
                 237 
                 98 
                 176 
               
               
                 24 
                 148 
                 52 
                 84 
                 100 
                 147 
                 21 
                 163 
                 93 
                 23 
                 5 
                 58 
                 164 
                 111 
                 185 
                 65 
                 66 
                 105 
                 186 
                 184 
                 26 
               
               
                 25 
                 154 
                 59 
                 90 
                 155 
                 58 
                 11 
                 170 
                 65 
                 171 
                 12 
                 64 
                 128 
                 86 
                 193 
                 113 
                 192 
                 33 
                 194 
                 133 
                 97 
               
               
                 26 
                 33 
                 161 
                 17 
                 122 
                 160 
                 84 
                 177 
                 72 
                 176 
                 178 
                 36 
                 8 
                 71 
                 200 
                 81 
                 121 
                 41 
                 21 
                 201 
                 141 
               
               
                 27 
                 166 
                 39 
                 71 
                 167 
                 103 
                 23 
                 78 
                 183 
                 43 
                 113 
                 15 
                 131 
                 185 
                 208 
                 89 
                 49 
                 209 
                 207 
                 29 
                 128 
               
               
                 28 
                 173 
                 77 
                 45 
                 172 
                 109 
                 125 
                 85 
                 50 
                 138 
                 190 
                 191 
                 64 
                 32 
                 216 
                 96 
                 97 
                 215 
                 217 
                 136 
                 56 
               
               
                 29 
                 115 
                 179 
                 51 
                 131 
                 178 
                 83 
                 92 
                 197 
                 127 
                 57 
                 113 
                 155 
                 198 
                 224 
                 223 
                 104 
                 144 
                 64 
                 164 
                 128 
               
               
                 30 
                 185 
                 89 
                 121 
                 137 
                 184 
                 70 
                 46 
                 99 
                 204 
                 205 
                 162 
                 64 
                 98 
                 232 
                 231 
                 72 
                 112 
                 152 
                 230 
                 52 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 20 
               
               
                   
               
               
                 Gr. Idx 
                   
                   
               
               
                 3RBs 
                 24RB 
                 25RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 9 
                 151 
                 150 
                 103 
                 80 
                 198 
                 10 
                 8 
                 221 
                 9 
                 10 
                 156 
                 107 
                 205 
                 229 
                 8 
                 68 
                 83 
               
               
                 2 
                 19 
                 207 
                 18 
                 17 
                 159 
                 89 
                 188 
                 75 
                 231 
                 19 
                 165 
                 18 
                 214 
                 92 
                 166 
                 20 
                 239 
                 136 
               
               
                 3 
                 28 
                 27 
                 169 
                 216 
                 122 
                 240 
                 26 
                 98 
                 84 
                 28 
                 175 
                 126 
                 27 
                 248 
                 29 
                 224 
                 102 
                 87 
               
               
                 4 
                 36 
                 37 
                 178 
                 225 
                 35 
                 131 
                 93 
                 249 
                 263 
                 38 
                 184 
                 135 
                 39 
                 136 
                 233 
                 37 
                 111 
                 155 
               
               
                 5 
                 140 
                 45 
                 234 
                 46 
                 187 
                 47 
                 272 
                 188 
                 258 
                 194 
                 48 
                 145 
                 47 
                 243 
                 193 
                 267 
                 242 
                 106 
               
               
                 6 
                 55 
                 196 
                 149 
                 197 
                 243 
                 56 
                 267 
                 54 
                 244 
                 56 
                 203 
                 252 
                 154 
                 130 
                 58 
                 155 
                 174 
                 57 
               
               
                 7 
                 65 
                 205 
                 158 
                 206 
                 253 
                 63 
                 65 
                 252 
                 135 
                 66 
                 213 
                 212 
                 164 
                 262 
                 261 
                 67 
                 286 
                 139 
               
               
                 8 
                 73 
                 214 
                 262 
                 74 
                 72 
                 168 
                 144 
                 215 
                 243 
                 76 
                 222 
                 75 
                 271 
                 173 
                 149 
                 77 
                 2 
                 17 
               
               
                 9 
                 82 
                 223 
                 81 
                 271 
                 177 
                 83 
                 176 
                 153 
                 224 
                 85 
                 231 
                 183 
                 12 
                 86 
                 280 
                 84 
                 281 
                 158 
               
               
                 10 
                 91 
                 280 
                 92 
                 90 
                 186 
                 232 
                 233 
                 21 
                 185 
                 95 
                 241 
                 192 
                 94 
                 168 
                 96 
                 21 
                 290 
                 93 
               
               
                 11 
                 242 
                 195 
                 6 
                 101 
                 99 
                 100 
                 30 
                 44 
                 102 
                 104 
                 250 
                 251 
                 6 
                 202 
                 103 
                 105 
                 31 
                 201 
               
               
                 12 
                 109 
                 110 
                 204 
                 39 
                 15 
                 251 
                 111 
                 180 
                 166 
                 113 
                 260 
                 211 
                 16 
                 112 
                 40 
                 114 
                 115 
                 187 
               
               
                 13 
                 119 
                 213 
                 260 
                 24 
                 120 
                 48 
                 118 
                 261 
                 232 
                 123 
                 269 
                 25 
                 270 
                 221 
                 196 
                 220 
                 122 
                 124 
               
               
                 14 
                 128 
                 33 
                 270 
                 34 
                 222 
                 269 
                 127 
                 129 
                 71 
                 132 
                 230 
                 133 
                 131 
                 279 
                 278 
                 34 
                 191 
                 35 
               
               
                 15 
                 137 
                 136 
                 138 
                 278 
                 66 
                 43 
                 231 
                 42 
                 208 
                 288 
                 142 
                 44 
                 239 
                 289 
                 240 
                 143 
                 83 
                 259 
               
               
                 16 
                 146 
                 147 
                 4 
                 145 
                 5 
                 217 
                 240 
                 52 
                 75 
                 5 
                 151 
                 249 
                 54 
                 4 
                 53 
                 34 
                 210 
                 150 
               
               
                 17 
                 155 
                 13 
                 249 
                 61 
                 14 
                 156 
                 154 
                 250 
                 212 
                 161 
                 63 
                 160 
                 162 
                 15 
                 14 
                 102 
                 259 
                 258 
               
               
                 18 
                 164 
                 70 
                 23 
                 259 
                 163 
                 165 
                 22 
                 51 
                 108 
                 170 
                 24 
                 268 
                 23 
                 72 
                 97 
                 73 
                 171 
                 169 
               
               
                 19 
                 174 
                 173 
                 32 
                 79 
                 172 
                 244 
                 268 
                 103 
                 117 
                 180 
                 33 
                 179 
                 82 
                 277 
                 181 
                 253 
                 178 
                 106 
               
               
                 20 
                 41 
                 183 
                 277 
                 182 
                 88 
                 184 
                 253 
                 239 
                 181 
                 189 
                 43 
                 42 
                 287 
                 91 
                 190 
                 188 
                 262 
                 92 
               
               
                 21 
                 192 
                 50 
                 3 
                 191 
                 193 
                 97 
                 262 
                 135 
                 98 
                 198 
                 52 
                 101 
                 199 
                 125 
                 200 
                 197 
                 3 
                 272 
               
               
                 22 
                 201 
                 60 
                 202 
                 12 
                 106 
                 59 
                 200 
                 107 
                 130 
                 208 
                 62 
                 110 
                 281 
                 207 
                 13 
                 209 
                 12 
                 135 
               
               
                 23 
                 210 
                 69 
                 21 
                 209 
                 211 
                 139 
                 68 
                 40 
                 97 
                 218 
                 71 
                 22 
                 120 
                 217 
                 144 
                 216 
                 291 
                 276 
               
               
                 24 
                 219 
                 78 
                 125 
                 77 
                 30 
                 220 
                 31 
                 218 
                 148 
                 227 
                 80 
                 81 
                 129 
                 228 
                 31 
                 32 
                 226 
                 7 
               
               
                 25 
                 87 
                 228 
                 134 
                 86 
                 40 
                 227 
                 39 
                 229 
                 16 
                 237 
                 90 
                 41 
                 139 
                 163 
                 235 
                 138 
                 236 
                 119 
               
               
                 26 
                 96 
                 143 
                 49 
                 237 
                 25 
                 238 
                 236 
                 11 
                 124 
                 99 
                 245 
                 148 
                 246 
                 50 
                 247 
                 100 
                 26 
                 51 
               
               
                 27 
                 247 
                 246 
                 105 
                 58 
                 248 
                 152 
                 190 
                 34 
                 20 
                 255 
                 109 
                 254 
                 158 
                 157 
                 60 
                 256 
                 182 
                 108 
               
               
                 28 
                 256 
                 114 
                 67 
                 161 
                 255 
                 185 
                 257 
                 43 
                 199 
                 265 
                 118 
                 167 
                 266 
                 45 
                 264 
                 69 
                 119 
                 191 
               
               
                 29 
                 264 
                 76 
                 265 
                 123 
                 266 
                 194 
                 124 
                 95 
                 208 
                 274 
                 128 
                 275 
                 127 
                 79 
                 273 
                 201 
                 157 
                 54 
               
               
                 30 
                 274 
                 132 
                 180 
                 85 
                 273 
                 275 
                 133 
                 104 
                 62 
                 284 
                 283 
                 137 
                 186 
                 88 
                 64 
                 282 
                 285 
                 210 
               
               
                   
               
             
          
         
       
     
         [0114]    In this case, if the maximum number of sequences per each group is predetermined to 5, the grouping can be performed as shown in the following tables 21 and 22. The tables 21 and 22 are also the case when the base sequences are selected by actual cross correlation calculation. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 21 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 25 
                 2 
                 20 
                 2 
                 3 
                 25 
                 57 
                 4 
                 75 
                 60 
                 79 
                 4 
               
               
                 2 
                 2 
                 3 
                 4 
                 40 
                 33 
                 65 
                 28 
                 7 
                 71 
                 96 
                 64 
                 45 
                 75 
               
               
                 3 
                 3 
                 14 
                 6 
                 7 
                 21 
                 53 
                 9 
                 46 
                 10 
                 37 
                 11 
                 39 
                 86 
               
               
                 4 
                 4 
                 6 
                 47 
                 9 
                 66 
                 56 
                 41 
                 14 
                 85 
                 78 
                 15 
                 71 
                 14 
               
               
                 5 
                 5 
                 39 
                 39 
                 47 
                 54 
                 44 
                 50 
                 71 
                 44 
                 60 
                 56 
                 75 
                 103 
               
               
                 6 
                 6 
                 9 
                 31 
                 61 
                 14 
                 17 
                 84 
                 21 
                 92 
                 85 
                 97 
                 50 
                 67 
               
               
                 7 
                 7 
                 42 
                 33 
                 16 
                 28 
                 20 
                 87 
                 24 
                 51 
                 60 
                 82 
                 63 
                 26 
               
               
                 8 
                 8 
                 12 
                 30 
                 42 
                 54 
                 23 
                 5 
                 28 
                 99 
                 49 
                 67 
                 86 
                 1 
               
               
                 9 
                 9 
                 45 
                 17 
                 68 
                 21 
                 48 
                 85 
                 31 
                 74 
                 58 
                 61 
                 89 
                 78 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 5 
                 73 
                 29 
                 106 
                 70 
                 34 
                 93 
                 112 
                 36 
               
               
                 11 
                 11 
                 1 
                 21 
                 11 
                 25 
                 32 
                 2 
                 38 
                 102 
                 11 
                 40 
                 78 
                 12 
               
               
                 12 
                 12 
                 37 
                 23 
                 51 
                 63 
                 79 
                 64 
                 95 
                 77 
                 41 
                 72 
                 44 
                 100 
               
               
                 13 
                 13 
                 4 
                 5 
                 6 
                 30 
                 67 
                 37 
                 45 
                 9 
                 18 
                 104 
                 47 
                 85 
               
               
                 14 
                 14 
                 21 
                 7 
                 32 
                 22 
                 40 
                 58 
                 102 
                 84 
                 48 
                 51 
                 6 
                 23 
               
               
                 15 
                 15 
                 23 
                 58 
                 58 
                 34 
                 43 
                 61 
                 105 
                 16 
                 25 
                 17 
                 111 
                 83 
               
               
                 16 
                 16 
                 24 
                 1 
                 13 
                 65 
                 46 
                 28 
                 91 
                 2 
                 82 
                 96 
                 2 
                 30 
               
               
                 17 
                 17 
                 26 
                 52 
                 39 
                 49 
                 31 
                 49 
                 23 
                 59 
                 16 
                 62 
                 107 
                 90 
               
               
                 18 
                 18 
                 43 
                 54 
                 65 
                 41 
                 22 
                 52 
                 62 
                 98 
                 89 
                 9 
                 66 
                 28 
               
               
                 19 
                 19 
                 29 
                 36 
                 8 
                 20 
                 10 
                 25 
                 30 
                 12 
                 87 
                 41 
                 24 
                 70 
               
               
                 20 
                 20 
                 46 
                 38 
                 46 
                 60 
                 87 
                 57 
                 69 
                 5 
                 96 
                 73 
                 35 
                 101 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 66 
                 16 
                 60 
                 1 
                 37 
                 73 
                 20 
                 1 
                 39 
               
               
                 22 
                 22 
                 2 
                 42 
                 3 
                 50 
                 41 
                 78 
                 76 
                 49 
                 33 
                 52 
                 24 
                 35 
               
               
                 23 
                 23 
                 35 
                 29 
                 29 
                 17 
                 66 
                 55 
                 79 
                 8 
                 58 
                 46 
                 27 
                 112 
               
               
                 24 
                 24 
                 5 
                 26 
                 55 
                 43 
                 69 
                 2 
                 83 
                 56 
                 47 
                 31 
                 12 
                 88 
               
               
                 25 
                 25 
                 38 
                 28 
                 10 
                 57 
                 72 
                 27 
                 15 
                 65 
                 86 
                 63 
                 46 
                 16 
               
               
                 26 
                 26 
                 8 
                 20 
                 24 
                 17 
                 45 
                 75 
                 63 
                 54 
                 90 
                 95 
                 57 
                 38 
               
               
                 27 
                 27 
                 41 
                 22 
                 62 
                 44 
                 33 
                 48 
                 93 
                 22 
                 29 
                 23 
                 98 
                 42 
               
               
                 28 
                 28 
                 33 
                 53 
                 64 
                 50 
                 36 
                 80 
                 61 
                 97 
                 70 
                 102 
                 57 
                 74 
               
               
                 29 
                 29 
                 44 
                 8 
                 31 
                 38 
                 24 
                 39 
                 100 
                 39 
                 11 
                 49 
                 68 
                 106 
               
               
                 30 
                 30 
                 22 
                 55 
                 69 
                 51 
                 86 
                 64 
                 50 
                 103 
                 18 
                 34 
                 109 
                 81 
               
               
                   
               
             
          
           
               
                   
                 Gr. Idx 
                   
                   
               
               
                   
                 3RBs 
                 12RB 
                 15RB 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 74 
                 51 
                 4 
                 5 
                 6 
                 95 
                 140 
                 125 
                 5 
               
               
                   
                 2 
                 9 
                 120 
                 44 
                 8 
                 101 
                 71 
                 131 
                 12 
                 11 
               
               
                   
                 3 
                 83 
                 13 
                 14 
                 48 
                 17 
                 107 
                 77 
                 18 
                 62 
               
               
                   
                 4 
                 18 
                 122 
                 87 
                 129 
                 23 
                 83 
                 113 
                 68 
                 24 
               
               
                   
                 5 
                 92 
                 23 
                 115 
                 78 
                 29 
                 118 
                 148 
                 28 
                 163 
               
               
                   
                 6 
                 27 
                 96 
                 131 
                 73 
                 35 
                 154 
                 124 
                 34 
                 94 
               
               
                   
                 7 
                 101 
                 124 
                 32 
                 66 
                 40 
                 130 
                 160 
                 41 
                 100 
               
               
                   
                 8 
                 36 
                 105 
                 8 
                 59 
                 46 
                 136 
                 106 
                 47 
                 91 
               
               
                   
                 9 
                 133 
                 110 
                 41 
                 75 
                 52 
                 141 
                 171 
                 142 
                 7 
               
               
                   
                 10 
                 45 
                 114 
                 91 
                 17 
                 58 
                 147 
                 57 
                 177 
                 13 
               
               
                   
                 11 
                 119 
                 3 
                 50 
                 77 
                 64 
                 153 
                 4 
                 63 
                 19 
               
               
                   
                 12 
                 54 
                 100 
                 123 
                 26 
                 69 
                 159 
                 129 
                 114 
                 10 
               
               
                   
                 13 
                 12 
                 58 
                 128 
                 114 
                 75 
                 165 
                 135 
                 120 
                 76 
               
               
                   
                 14 
                 63 
                 132 
                 7 
                 35 
                 81 
                 21 
                 170 
                 36 
                 80 
               
               
                   
                 15 
                 67 
                 137 
                 21 
                 68 
                 86 
                 27 
                 176 
                 146 
                 42 
               
               
                   
                 16 
                 2 
                 118 
                 71 
                 16 
                 93 
                 152 
                 3 
                 33 
                 137 
               
               
                   
                 17 
                 7 
                 76 
                 77 
                 132 
                 158 
                 98 
                 9 
                 143 
                 134 
               
               
                   
                 18 
                 11 
                 127 
                 81 
                 25 
                 104 
                 14 
                 44 
                 59 
                 103 
               
               
                   
                 19 
                 85 
                 39 
                 16 
                 113 
                 20 
                 50 
                 110 
                 65 
                 169 
               
               
                   
                 20 
                 136 
                 20 
                 89 
                 43 
                 115 
                 26 
                 175 
                 116 
                 71 
               
               
                   
                 21 
                 94 
                 48 
                 25 
                 129 
                 121 
                 32 
                 122 
                 2 
                 166 
               
               
                   
                 22 
                 6 
                 64 
                 52 
                 99 
                 127 
                 38 
                 8 
                 172 
                 67 
               
               
                   
                 23 
                 103 
                 34 
                 131 
                 80 
                 133 
                 73 
                 132 
                 88 
                 43 
               
               
                   
                 24 
                 38 
                 15 
                 73 
                 108 
                 139 
                 49 
                 19 
                 138 
                 79 
               
               
                   
                 25 
                 112 
                 66 
                 43 
                 113 
                 144 
                 25 
                 55 
                 145 
                 85 
               
               
                   
                 26 
                 47 
                 116 
                 24 
                 61 
                 150 
                 61 
                 31 
                 151 
                 16 
               
               
                   
                 27 
                 121 
                 75 
                 52 
                 17 
                 156 
                 96 
                 155 
                 66 
                 111 
               
               
                   
                 28 
                 56 
                 79 
                 126 
                 125 
                 162 
                 72 
                 102 
                 42 
                 161 
               
               
                   
                 29 
                 130 
                 95 
                 19 
                 131 
                 78 
                 48 
                 108 
                 167 
                 168 
               
               
                   
                 30 
                 65 
                 135 
                 134 
                 100 
                 173 
                 54 
                 84 
                 39 
                 174 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 22 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
               
               
                 3RBs 
                 16RB 
                 18RB 
                 20RB 
               
               
                   
               
             
          
           
               
                 1 
                 6 
                 102 
                 70 
                 54 
                 7 
                 112 
                 7 
                 6 
                 165 
                 49 
                 8 
                 7 
                 167 
                 127 
                 87 
               
               
                 2 
                 76 
                 12 
                 108 
                 140 
                 60 
                 119 
                 14 
                 84 
                 154 
                 98 
                 15 
                 135 
                 95 
                 175 
                 75 
               
               
                 3 
                 18 
                 114 
                 19 
                 82 
                 66 
                 20 
                 126 
                 91 
                 161 
                 21 
                 23 
                 143 
                 103 
                 24 
                 142 
               
               
                 4 
                 25 
                 152 
                 120 
                 24 
                 88 
                 133 
                 28 
                 168 
                 98 
                 196 
                 31 
                 150 
                 190 
                 30 
                 32 
               
               
                 5 
                 30 
                 158 
                 174 
                 69 
                 31 
                 34 
                 175 
                 139 
                 33 
                 35 
                 39 
                 38 
                 158 
                 118 
                 218 
               
               
                 6 
                 37 
                 132 
                 101 
                 133 
                 180 
                 41 
                 146 
                 40 
                 199 
                 182 
                 46 
                 126 
                 47 
                 45 
                 106 
               
               
                 7 
                 43 
                 139 
                 107 
                 91 
                 44 
                 48 
                 153 
                 118 
                 188 
                 206 
                 54 
                 174 
                 173 
                 134 
                 53 
               
               
                 8 
                 49 
                 113 
                 145 
                 50 
                 97 
                 54 
                 195 
                 139 
                 181 
                 2 
                 62 
                 181 
                 221 
                 61 
                 2 
               
               
                 9 
                 151 
                 103 
                 56 
                 132 
                 183 
                 61 
                 202 
                 62 
                 132 
                 114 
                 69 
                 189 
                 70 
                 149 
                 129 
               
               
                 10 
                 62 
                 157 
                 189 
                 61 
                 14 
                 68 
                 174 
                 209 
                 173 
                 138 
                 77 
                 197 
                 157 
                 196 
                 76 
               
               
                 11 
                 68 
                 67 
                 163 
                 20 
                 106 
                 75 
                 74 
                 76 
                 5 
                 181 
                 85 
                 204 
                 5 
                 84 
                 164 
               
               
                 12 
                 74 
                 169 
                 10 
                 138 
                 170 
                 187 
                 152 
                 81 
                 82 
                 166 
                 92 
                 13 
                 172 
                 33 
                 152 
               
               
                 13 
                 80 
                 176 
                 81 
                 144 
                 79 
                 194 
                 36 
                 141 
                 159 
                 18 
                 220 
                 180 
                 101 
                 21 
                 100 
               
               
                 14 
                 86 
                 150 
                 182 
                 87 
                 10 
                 95 
                 201 
                 25 
                 96 
                 11 
                 108 
                 107 
                 109 
                 188 
                 228 
               
               
                 15 
                 188 
                 93 
                 29 
                 156 
                 92 
                 102 
                 208 
                 32 
                 103 
                 172 
                 116 
                 36 
                 235 
                 115 
                 195 
               
               
                 16 
                 3 
                 98 
                 162 
                 35 
                 99 
                 109 
                 3 
                 179 
                 56 
                 110 
                 123 
                 203 
                 4 
                 124 
                 44 
               
               
                 17 
                 105 
                 41 
                 9 
                 104 
                 181 
                 116 
                 10 
                 186 
                 115 
                 200 
                 131 
                 132 
                 130 
                 51 
                 11 
               
               
                 18 
                 111 
                 47 
                 15 
                 110 
                 175 
                 17 
                 175 
                 70 
                 52 
                 193 
                 19 
                 59 
                 138 
                 139 
                 218 
               
               
                 19 
                 117 
                 22 
                 181 
                 21 
                 116 
                 24 
                 59 
                 130 
                 182 
                 129 
                 27 
                 147 
                 146 
                 226 
                 206 
               
               
                 20 
                 28 
                 123 
                 124 
                 171 
                 85 
                 136 
                 31 
                 137 
                 135 
                 206 
                 35 
                 154 
                 234 
                 155 
                 214 
               
               
                 21 
                 129 
                 34 
                 2 
                 66 
                 130 
                 143 
                 37 
                 2 
                 73 
                 142 
                 162 
                 42 
                 82 
                 43 
                 163 
               
               
                 22 
                 135 
                 136 
                 59 
                 8 
                 183 
                 150 
                 9 
                 149 
                 44 
                 79 
                 170 
                 169 
                 50 
                 90 
                 110 
               
               
                 23 
                 142 
                 78 
                 46 
                 94 
                 141 
                 16 
                 30 
                 209 
                 157 
                 72 
                 58 
                 177 
                 18 
                 178 
                 237 
               
               
                 24 
                 148 
                 52 
                 84 
                 100 
                 147 
                 163 
                 93 
                 23 
                 5 
                 58 
                 185 
                 65 
                 66 
                 105 
                 186 
               
               
                 25 
                 154 
                 59 
                 90 
                 155 
                 58 
                 170 
                 65 
                 171 
                 12 
                 64 
                 193 
                 113 
                 192 
                 33 
                 194 
               
               
                 26 
                 33 
                 161 
                 17 
                 122 
                 160 
                 177 
                 72 
                 176 
                 178 
                 36 
                 200 
                 81 
                 121 
                 41 
                 21 
               
               
                 27 
                 166 
                 39 
                 71 
                 167 
                 103 
                 78 
                 183 
                 43 
                 113 
                 15 
                 208 
                 89 
                 49 
                 209 
                 207 
               
               
                 28 
                 173 
                 77 
                 45 
                 172 
                 109 
                 85 
                 50 
                 138 
                 190 
                 191 
                 216 
                 96 
                 97 
                 215 
                 217 
               
               
                 29 
                 115 
                 179 
                 51 
                 131 
                 178 
                 92 
                 197 
                 127 
                 57 
                 113 
                 224 
                 223 
                 104 
                 144 
                 64 
               
               
                 30 
                 185 
                 89 
                 121 
                 137 
                 184 
                 46 
                 99 
                 204 
                 205 
                 162 
                 232 
                 231 
                 72 
                 112 
                 152 
               
               
                   
               
             
          
           
               
                   
                 Gr. Idx 
                   
                   
               
               
                   
                 3RBs 
                 24RB 
                 25RBs 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 9 
                 151 
                 150 
                 103 
                 80 
                 9 
                 10 
                 156 
                 107 
                 205 
               
               
                   
                 2 
                 19 
                 207 
                 18 
                 17 
                 159 
                 19 
                 165 
                 18 
                 214 
                 92 
               
               
                   
                 3 
                 28 
                 27 
                 169 
                 216 
                 122 
                 28 
                 175 
                 126 
                 27 
                 248 
               
               
                   
                 4 
                 36 
                 37 
                 178 
                 225 
                 35 
                 38 
                 184 
                 135 
                 39 
                 136 
               
               
                   
                 5 
                 140 
                 45 
                 234 
                 46 
                 187 
                 194 
                 48 
                 145 
                 47 
                 243 
               
               
                   
                 6 
                 55 
                 196 
                 149 
                 197 
                 243 
                 56 
                 203 
                 252 
                 154 
                 130 
               
               
                   
                 7 
                 64 
                 205 
                 158 
                 206 
                 253 
                 66 
                 213 
                 212 
                 164 
                 262 
               
               
                   
                 8 
                 73 
                 214 
                 262 
                 74 
                 72 
                 76 
                 222 
                 75 
                 271 
                 173 
               
               
                   
                 9 
                 82 
                 223 
                 81 
                 271 
                 177 
                 85 
                 231 
                 183 
                 12 
                 86 
               
               
                   
                 10 
                 91 
                 280 
                 92 
                 90 
                 186 
                 95 
                 241 
                 192 
                 94 
                 168 
               
               
                   
                 11 
                 242 
                 195 
                 6 
                 101 
                 99 
                 104 
                 250 
                 251 
                 6 
                 202 
               
               
                   
                 12 
                 109 
                 110 
                 204 
                 39 
                 15 
                 113 
                 260 
                 211 
                 16 
                 112 
               
               
                   
                 13 
                 119 
                 213 
                 260 
                 24 
                 120 
                 123 
                 269 
                 25 
                 270 
                 221 
               
               
                   
                 14 
                 128 
                 33 
                 270 
                 34 
                 222 
                 132 
                 230 
                 133 
                 131 
                 279 
               
               
                   
                 15 
                 137 
                 136 
                 138 
                 278 
                 66 
                 288 
                 142 
                 44 
                 239 
                 289 
               
               
                   
                 16 
                 146 
                 147 
                 4 
                 145 
                 5 
                 5 
                 151 
                 249 
                 54 
                 4 
               
               
                   
                 17 
                 155 
                 13 
                 249 
                 61 
                 14 
                 161 
                 63 
                 160 
                 162 
                 15 
               
               
                   
                 18 
                 164 
                 70 
                 23 
                 259 
                 163 
                 170 
                 24 
                 268 
                 23 
                 72 
               
               
                   
                 19 
                 174 
                 173 
                 32 
                 79 
                 172 
                 180 
                 33 
                 179 
                 82 
                 277 
               
               
                   
                 20 
                 41 
                 183 
                 277 
                 182 
                 88 
                 189 
                 43 
                 42 
                 287 
                 91 
               
               
                   
                 21 
                 192 
                 50 
                 3 
                 191 
                 193 
                 198 
                 52 
                 101 
                 199 
                 125 
               
               
                   
                 22 
                 201 
                 60 
                 202 
                 12 
                 106 
                 208 
                 62 
                 110 
                 281 
                 207 
               
               
                   
                 23 
                 210 
                 69 
                 21 
                 209 
                 211 
                 218 
                 71 
                 22 
                 120 
                 217 
               
               
                   
                 24 
                 219 
                 78 
                 125 
                 77 
                 30 
                 227 
                 80 
                 81 
                 129 
                 228 
               
               
                   
                 25 
                 87 
                 228 
                 134 
                 86 
                 40 
                 237 
                 90 
                 41 
                 139 
                 163 
               
               
                   
                 26 
                 96 
                 143 
                 49 
                 237 
                 25 
                 99 
                 245 
                 148 
                 246 
                 50 
               
               
                   
                 27 
                 247 
                 246 
                 105 
                 58 
                 248 
                 255 
                 109 
                 254 
                 158 
                 157 
               
               
                   
                 28 
                 256 
                 114 
                 67 
                 161 
                 255 
                 265 
                 118 
                 167 
                 266 
                 45 
               
               
                   
                 29 
                 264 
                 76 
                 265 
                 123 
                 266 
                 274 
                 128 
                 275 
                 127 
                 79 
               
               
                   
                 30 
                 274 
                 132 
                 180 
                 85 
                 273 
                 284 
                 283 
                 137 
                 186 
                 88 
               
               
                   
                   
               
             
          
         
       
     
         [0115]    In another example, if the maximum number of sequences per each group is predetermined to 4, the grouping can be performed as shown in the following tables 23 and 24. The tables 23 and 24 are also the case when the base sequences are selected by actual cross correlation calculation. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 23 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 25 
                 2 
                 20 
                 2 
                 3 
                 25 
                 57 
                 4 
                 75 
                 60 
                 79 
                 4 
               
               
                 2 
                 2 
                 3 
                 4 
                 40 
                 33 
                 65 
                 28 
                 7 
                 71 
                 96 
                 64 
                 45 
                 75 
               
               
                 3 
                 3 
                 14 
                 6 
                 7 
                 21 
                 53 
                 9 
                 46 
                 10 
                 37 
                 11 
                 39 
                 86 
               
               
                 4 
                 4 
                 6 
                 47 
                 9 
                 66 
                 56 
                 41 
                 14 
                 85 
                 78 
                 15 
                 71 
                 14 
               
               
                 5 
                 5 
                 39 
                 39 
                 47 
                 54 
                 44 
                 50 
                 71 
                 44 
                 60 
                 56 
                 75 
                 103 
               
               
                 6 
                 6 
                 9 
                 31 
                 61 
                 14 
                 17 
                 84 
                 21 
                 92 
                 85 
                 97 
                 50 
                 67 
               
               
                 7 
                 7 
                 42 
                 33 
                 16 
                 28 
                 20 
                 87 
                 24 
                 51 
                 60 
                 82 
                 63 
                 26 
               
               
                 8 
                 8 
                 12 
                 30 
                 42 
                 54 
                 23 
                 5 
                 28 
                 99 
                 49 
                 67 
                 86 
                 1 
               
               
                 9 
                 9 
                 45 
                 17 
                 68 
                 21 
                 48 
                 85 
                 31 
                 74 
                 58 
                 61 
                 89 
                 78 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 5 
                 73 
                 29 
                 106 
                 70 
                 34 
                 93 
                 112 
                 36 
               
               
                 11 
                 11 
                 1 
                 21 
                 11 
                 25 
                 32 
                 2 
                 38 
                 102 
                 11 
                 40 
                 78 
                 12 
               
               
                 12 
                 12 
                 37 
                 23 
                 51 
                 63 
                 79 
                 64 
                 95 
                 77 
                 41 
                 72 
                 44 
                 100 
               
               
                 13 
                 13 
                 4 
                 5 
                 6 
                 30 
                 67 
                 37 
                 45 
                 9 
                 18 
                 104 
                 47 
                 85 
               
               
                 14 
                 14 
                 21 
                 7 
                 32 
                 22 
                 40 
                 58 
                 102 
                 84 
                 48 
                 51 
                 6 
                 23 
               
               
                 15 
                 15 
                 23 
                 58 
                 58 
                 34 
                 43 
                 61 
                 105 
                 16 
                 25 
                 17 
                 111 
                 83 
               
               
                 16 
                 16 
                 24 
                 1 
                 13 
                 65 
                 46 
                 28 
                 91 
                 2 
                 82 
                 96 
                 2 
                 30 
               
               
                 17 
                 17 
                 26 
                 52 
                 39 
                 49 
                 31 
                 49 
                 23 
                 59 
                 16 
                 62 
                 107 
                 90 
               
               
                 18 
                 18 
                 43 
                 54 
                 65 
                 41 
                 22 
                 52 
                 62 
                 98 
                 89 
                 9 
                 66 
                 28 
               
               
                 19 
                 19 
                 29 
                 36 
                 8 
                 20 
                 10 
                 25 
                 30 
                 12 
                 87 
                 41 
                 24 
                 70 
               
               
                 20 
                 20 
                 46 
                 38 
                 46 
                 60 
                 87 
                 57 
                 69 
                 5 
                 96 
                 73 
                 35 
                 101 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 66 
                 16 
                 60 
                 1 
                 37 
                 73 
                 20 
                 1 
                 39 
               
               
                 22 
                 22 
                 2 
                 42 
                 3 
                 50 
                 41 
                 78 
                 76 
                 49 
                 33 
                 52 
                 24 
                 35 
               
               
                 23 
                 23 
                 35 
                 29 
                 29 
                 17 
                 66 
                 55 
                 79 
                 8 
                 58 
                 46 
                 27 
                 112 
               
               
                 24 
                 24 
                 5 
                 26 
                 55 
                 43 
                 69 
                 2 
                 83 
                 56 
                 47 
                 31 
                 12 
                 88 
               
               
                 25 
                 25 
                 38 
                 28 
                 10 
                 57 
                 72 
                 27 
                 15 
                 65 
                 86 
                 63 
                 46 
                 16 
               
               
                 26 
                 26 
                 8 
                 20 
                 24 
                 17 
                 45 
                 75 
                 63 
                 54 
                 90 
                 95 
                 57 
                 38 
               
               
                 27 
                 27 
                 41 
                 22 
                 62 
                 44 
                 33 
                 48 
                 93 
                 22 
                 29 
                 23 
                 98 
                 42 
               
               
                 28 
                 28 
                 33 
                 53 
                 64 
                 50 
                 36 
                 80 
                 61 
                 97 
                 70 
                 102 
                 57 
                 74 
               
               
                 29 
                 29 
                 44 
                 8 
                 31 
                 38 
                 24 
                 39 
                 100 
                 36 
                 11 
                 49 
                 68 
                 106 
               
               
                 30 
                 30 
                 22 
                 55 
                 69 
                 51 
                 86 
                 64 
                 50 
                 103 
                 18 
                 34 
                 109 
                 81 
               
               
                   
               
             
          
           
               
                   
                 Gr. Idx 
                   
                   
               
               
                   
                 3RBs 
                 12RB 
                 15RB 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 74 
                 51 
                 4 
                 5 
                 6 
                 95 
                 140 
                 125 
               
               
                   
                 2 
                 9 
                 120 
                 44 
                 8 
                 101 
                 71 
                 131 
                 12 
               
               
                   
                 3 
                 83 
                 13 
                 14 
                 48 
                 17 
                 107 
                 77 
                 18 
               
               
                   
                 4 
                 18 
                 122 
                 87 
                 129 
                 23 
                 83 
                 113 
                 68 
               
               
                   
                 5 
                 92 
                 23 
                 115 
                 78 
                 29 
                 118 
                 148 
                 28 
               
               
                   
                 6 
                 27 
                 96 
                 131 
                 73 
                 35 
                 154 
                 124 
                 34 
               
               
                   
                 7 
                 101 
                 124 
                 32 
                 66 
                 40 
                 130 
                 160 
                 41 
               
               
                   
                 8 
                 36 
                 105 
                 8 
                 59 
                 46 
                 136 
                 106 
                 47 
               
               
                   
                 9 
                 133 
                 110 
                 41 
                 75 
                 52 
                 141 
                 171 
                 142 
               
               
                   
                 10 
                 45 
                 114 
                 91 
                 17 
                 58 
                 147 
                 57 
                 177 
               
               
                   
                 11 
                 119 
                 3 
                 50 
                 77 
                 64 
                 153 
                 4 
                 63 
               
               
                   
                 12 
                 54 
                 100 
                 123 
                 26 
                 69 
                 159 
                 129 
                 114 
               
               
                   
                 13 
                 12 
                 58 
                 128 
                 114 
                 75 
                 165 
                 135 
                 120 
               
               
                   
                 14 
                 63 
                 132 
                 7 
                 35 
                 81 
                 21 
                 170 
                 36 
               
               
                   
                 15 
                 67 
                 137 
                 21 
                 68 
                 86 
                 27 
                 176 
                 146 
               
               
                   
                 16 
                 2 
                 118 
                 71 
                 16 
                 93 
                 152 
                 3 
                 33 
               
               
                   
                 17 
                 7 
                 76 
                 77 
                 132 
                 158 
                 98 
                 9 
                 143 
               
               
                   
                 18 
                 11 
                 127 
                 81 
                 25 
                 104 
                 14 
                 44 
                 59 
               
               
                   
                 19 
                 85 
                 39 
                 16 
                 113 
                 20 
                 50 
                 110 
                 65 
               
               
                   
                 20 
                 136 
                 20 
                 89 
                 43 
                 115 
                 26 
                 175 
                 116 
               
               
                   
                 21 
                 94 
                 48 
                 25 
                 129 
                 121 
                 32 
                 122 
                 2 
               
               
                   
                 22 
                 6 
                 64 
                 52 
                 99 
                 127 
                 38 
                 8 
                 172 
               
               
                   
                 23 
                 103 
                 34 
                 131 
                 80 
                 133 
                 73 
                 132 
                 88 
               
               
                   
                 24 
                 38 
                 15 
                 73 
                 108 
                 139 
                 49 
                 19 
                 138 
               
               
                   
                 25 
                 112 
                 66 
                 43 
                 113 
                 144 
                 25 
                 55 
                 145 
               
               
                   
                 26 
                 47 
                 116 
                 24 
                 61 
                 150 
                 61 
                 31 
                 151 
               
               
                   
                 27 
                 121 
                 75 
                 52 
                 17 
                 156 
                 96 
                 155 
                 66 
               
               
                   
                 28 
                 56 
                 79 
                 126 
                 125 
                 162 
                 72 
                 102 
                 42 
               
               
                   
                 29 
                 130 
                 95 
                 19 
                 131 
                 78 
                 48 
                 180 
                 167 
               
               
                   
                 30 
                 65 
                 135 
                 134 
                 100 
                 173 
                 54 
                 84 
                 39 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 24 
               
               
                   
               
               
                 Gr. 
                   
                   
                   
                   
                   
               
               
                 Idx 
               
               
                 3RBs 
                 3RB 
                 18RB 
                 20RB 
                 24RB 
                 25RBs 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 6 
                 102 
                 70 
                 54 
                 112 
                 7 
                 6 
                 165 
                 8 
                 7 
                 167 
                 127 
                 9 
                 151 
                 150 
                 103 
                 9 
                 10 
                 156 
                 107 
               
               
                 2 
                 76 
                 12 
                 108 
                 140 
                 119 
                 14 
                 84 
                 154 
                 15 
                 135 
                 95 
                 175 
                 19 
                 207 
                 18 
                 17 
                 19 
                 165 
                 18 
                 214 
               
               
                 3 
                 18 
                 114 
                 19 
                 82 
                 20 
                 126 
                 91 
                 161 
                 23 
                 143 
                 103 
                 24 
                 28 
                 27 
                 169 
                 216 
                 28 
                 175 
                 126 
                 27 
               
               
                 4 
                 25 
                 152 
                 120 
                 24 
                 133 
                 28 
                 168 
                 98 
                 31 
                 150 
                 190 
                 30 
                 36 
                 37 
                 178 
                 225 
                 38 
                 184 
                 135 
                 39 
               
               
                 5 
                 30 
                 158 
                 174 
                 69 
                 34 
                 175 
                 139 
                 33 
                 39 
                 38 
                 158 
                 118 
                 140 
                 45 
                 234 
                 46 
                 194 
                 48 
                 145 
                 47 
               
               
                 6 
                 37 
                 132 
                 101 
                 133 
                 41 
                 146 
                 40 
                 199 
                 46 
                 126 
                 47 
                 45 
                 55 
                 196 
                 149 
                 197 
                 56 
                 203 
                 252 
                 154 
               
               
                 7 
                 43 
                 139 
                 107 
                 91 
                 48 
                 153 
                 118 
                 188 
                 54 
                 174 
                 173 
                 134 
                 64 
                 205 
                 158 
                 206 
                 66 
                 213 
                 212 
                 164 
               
               
                 8 
                 49 
                 113 
                 145 
                 50 
                 54 
                 195 
                 139 
                 181 
                 62 
                 181 
                 221 
                 61 
                 73 
                 214 
                 262 
                 74 
                 76 
                 222 
                 75 
                 271 
               
               
                 9 
                 151 
                 103 
                 56 
                 132 
                 61 
                 202 
                 62 
                 132 
                 69 
                 189 
                 70 
                 149 
                 82 
                 223 
                 81 
                 271 
                 85 
                 231 
                 183 
                 12 
               
               
                 10 
                 62 
                 157 
                 189 
                 61 
                 68 
                 174 
                 209 
                 173 
                 77 
                 197 
                 157 
                 196 
                 91 
                 280 
                 92 
                 90 
                 95 
                 241 
                 192 
                 94 
               
               
                 11 
                 68 
                 67 
                 163 
                 20 
                 75 
                 74 
                 76 
                 5 
                 85 
                 204 
                 5 
                 84 
                 242 
                 195 
                 6 
                 101 
                 104 
                 250 
                 251 
                 6 
               
               
                 12 
                 74 
                 169 
                 10 
                 138 
                 187 
                 152 
                 81 
                 82 
                 92 
                 13 
                 172 
                 33 
                 109 
                 110 
                 204 
                 39 
                 113 
                 260 
                 211 
                 16 
               
               
                 13 
                 80 
                 176 
                 81 
                 144 
                 194 
                 36 
                 141 
                 159 
                 220 
                 180 
                 101 
                 21 
                 119 
                 213 
                 260 
                 24 
                 123 
                 269 
                 25 
                 270 
               
               
                 14 
                 86 
                 150 
                 182 
                 87 
                 95 
                 201 
                 25 
                 96 
                 108 
                 107 
                 109 
                 188 
                 128 
                 33 
                 270 
                 34 
                 132 
                 230 
                 133 
                 131 
               
               
                 15 
                 188 
                 93 
                 29 
                 156 
                 102 
                 208 
                 32 
                 103 
                 116 
                 36 
                 235 
                 115 
                 137 
                 136 
                 138 
                 278 
                 288 
                 142 
                 44 
                 239 
               
               
                 16 
                 3 
                 98 
                 162 
                 35 
                 109 
                 3 
                 179 
                 56 
                 123 
                 203 
                 4 
                 124 
                 146 
                 147 
                 4 
                 145 
                 5 
                 151 
                 249 
                 54 
               
               
                 17 
                 105 
                 41 
                 9 
                 104 
                 116 
                 10 
                 186 
                 115 
                 131 
                 132 
                 130 
                 51 
                 155 
                 13 
                 249 
                 61 
                 161 
                 63 
                 160 
                 162 
               
               
                 18 
                 111 
                 47 
                 15 
                 110 
                 17 
                 175 
                 70 
                 52 
                 19 
                 59 
                 138 
                 139 
                 164 
                 70 
                 23 
                 259 
                 170 
                 24 
                 268 
                 23 
               
               
                 19 
                 117 
                 22 
                 181 
                 21 
                 24 
                 59 
                 130 
                 182 
                 27 
                 147 
                 146 
                 226 
                 174 
                 173 
                 32 
                 79 
                 180 
                 33 
                 179 
                 82 
               
               
                 20 
                 28 
                 123 
                 124 
                 171 
                 136 
                 31 
                 137 
                 135 
                 35 
                 154 
                 234 
                 155 
                 41 
                 183 
                 277 
                 182 
                 189 
                 43 
                 42 
                 287 
               
               
                 21 
                 129 
                 34 
                 2 
                 66 
                 143 
                 37 
                 2 
                 73 
                 162 
                 42 
                 82 
                 43 
                 192 
                 50 
                 3 
                 191 
                 198 
                 52 
                 101 
                 199 
               
               
                 22 
                 135 
                 136 
                 59 
                 8 
                 150 
                 9 
                 149 
                 44 
                 170 
                 169 
                 50 
                 90 
                 201 
                 60 
                 202 
                 12 
                 208 
                 62 
                 110 
                 281 
               
               
                 23 
                 142 
                 78 
                 46 
                 94 
                 16 
                 30 
                 209 
                 157 
                 58 
                 177 
                 18 
                 178 
                 210 
                 69 
                 21 
                 209 
                 218 
                 71 
                 22 
                 120 
               
               
                 24 
                 148 
                 52 
                 84 
                 100 
                 163 
                 93 
                 23 
                 5 
                 185 
                 65 
                 66 
                 105 
                 219 
                 78 
                 125 
                 77 
                 227 
                 80 
                 81 
                 129 
               
               
                 25 
                 154 
                 59 
                 90 
                 155 
                 170 
                 65 
                 171 
                 12 
                 193 
                 113 
                 192 
                 33 
                 87 
                 228 
                 134 
                 86 
                 237 
                 90 
                 41 
                 139 
               
               
                 26 
                 33 
                 161 
                 17 
                 122 
                 177 
                 72 
                 176 
                 178 
                 200 
                 81 
                 121 
                 41 
                 96 
                 143 
                 49 
                 237 
                 99 
                 245 
                 148 
                 246 
               
               
                 27 
                 166 
                 39 
                 71 
                 167 
                 78 
                 183 
                 43 
                 113 
                 208 
                 89 
                 49 
                 209 
                 247 
                 246 
                 105 
                 58 
                 255 
                 109 
                 254 
                 158 
               
               
                 28 
                 173 
                 77 
                 45 
                 172 
                 85 
                 50 
                 138 
                 190 
                 216 
                 96 
                 97 
                 215 
                 256 
                 114 
                 67 
                 161 
                 265 
                 118 
                 167 
                 266 
               
               
                 29 
                 115 
                 179 
                 51 
                 131 
                 92 
                 197 
                 127 
                 57 
                 224 
                 223 
                 104 
                 144 
                 264 
                 76 
                 265 
                 123 
                 274 
                 128 
                 275 
                 127 
               
               
                 30 
                 185 
                 89 
                 121 
                 137 
                 46 
                 99 
                 204 
                 205 
                 232 
                 231 
                 72 
                 112 
                 274 
                 132 
                 180 
                 85 
                 284 
                 283 
                 137 
                 186 
               
               
                   
               
             
          
         
       
     
         [0116]    In another example, if the maximum number of sequences per each group is predetermined to 3, the grouping can be performed as shown in the following tables 25 and 26. The tables 25 and 26 are also the case when the base sequences are selected by actual cross correlation calculation. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 25 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                   
                 10RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 25 
                 2 
                 20 
                 2 
                 3 
                 25 
                 57 
                 4 
                 75 
                 60 
                 79 
                 4 
               
               
                 2 
                 2 
                 3 
                 4 
                 40 
                 33 
                 65 
                 28 
                 7 
                 71 
                 96 
                 64 
                 45 
                 75 
               
               
                 3 
                 3 
                 14 
                 6 
                 7 
                 21 
                 53 
                 9 
                 46 
                 10 
                 37 
                 11 
                 39 
                 86 
               
               
                 4 
                 4 
                 6 
                 47 
                 9 
                 66 
                 56 
                 41 
                 14 
                 85 
                 78 
                 15 
                 71 
                 14 
               
               
                 5 
                 5 
                 39 
                 39 
                 47 
                 54 
                 44 
                 50 
                 71 
                 44 
                 60 
                 56 
                 75 
                 103 
               
               
                 6 
                 6 
                 9 
                 31 
                 61 
                 14 
                 17 
                 84 
                 21 
                 92 
                 85 
                 97 
                 50 
                 67 
               
               
                 7 
                 7 
                 42 
                 33 
                 16 
                 28 
                 20 
                 87 
                 24 
                 51 
                 60 
                 82 
                 63 
                 26 
               
               
                 8 
                 8 
                 12 
                 30 
                 42 
                 54 
                 23 
                 5 
                 28 
                 99 
                 49 
                 67 
                 86 
                 1 
               
               
                 9 
                 9 
                 45 
                 17 
                 68 
                 21 
                 48 
                 85 
                 31 
                 74 
                 58 
                 61 
                 89 
                 78 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 5 
                 73 
                 29 
                 106 
                 70 
                 34 
                 93 
                 112 
                 36 
               
               
                 11 
                 11 
                 1 
                 21 
                 11 
                 25 
                 32 
                 2 
                 38 
                 102 
                 11 
                 40 
                 78 
                 12 
               
               
                 12 
                 12 
                 37 
                 23 
                 51 
                 63 
                 79 
                 64 
                 95 
                 77 
                 41 
                 72 
                 44 
                 100 
               
               
                 13 
                 13 
                 4 
                 5 
                 6 
                 30 
                 67 
                 37 
                 45 
                 9 
                 18 
                 104 
                 47 
                 85 
               
               
                 14 
                 14 
                 21 
                 7 
                 32 
                 22 
                 40 
                 58 
                 102 
                 84 
                 48 
                 51 
                 6 
                 23 
               
               
                 15 
                 15 
                 23 
                 58 
                 58 
                 34 
                 43 
                 61 
                 105 
                 16 
                 25 
                 17 
                 111 
                 83 
               
               
                 16 
                 16 
                 24 
                 1 
                 13 
                 65 
                 46 
                 28 
                 91 
                 2 
                 82 
                 96 
                 2 
                 30 
               
               
                 17 
                 17 
                 26 
                 52 
                 39 
                 49 
                 31 
                 49 
                 23 
                 59 
                 16 
                 62 
                 107 
                 90 
               
               
                 18 
                 18 
                 43 
                 54 
                 65 
                 41 
                 22 
                 52 
                 62 
                 98 
                 89 
                 9 
                 66 
                 28 
               
               
                 19 
                 19 
                 29 
                 36 
                 8 
                 20 
                 10 
                 25 
                 30 
                 12 
                 87 
                 41 
                 24 
                 70 
               
               
                 20 
                 20 
                 46 
                 38 
                 46 
                 60 
                 87 
                 57 
                 69 
                 5 
                 96 
                 73 
                 35 
                 101 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 66 
                 16 
                 60 
                 1 
                 37 
                 73 
                 20 
                 1 
                 39 
               
               
                 22 
                 22 
                 2 
                 42 
                 3 
                 50 
                 41 
                 78 
                 76 
                 49 
                 33 
                 52 
                 24 
                 35 
               
               
                 23 
                 23 
                 35 
                 29 
                 29 
                 17 
                 66 
                 55 
                 79 
                 8 
                 58 
                 46 
                 27 
                 112 
               
               
                 24 
                 24 
                 5 
                 26 
                 55 
                 43 
                 69 
                 2 
                 83 
                 56 
                 47 
                 31 
                 12 
                 88 
               
               
                 25 
                 25 
                 38 
                 28 
                 10 
                 57 
                 72 
                 27 
                 15 
                 65 
                 86 
                 63 
                 46 
                 16 
               
               
                 26 
                 26 
                 8 
                 20 
                 24 
                 17 
                 45 
                 75 
                 63 
                 54 
                 90 
                 95 
                 57 
                 38 
               
               
                 27 
                 27 
                 41 
                 22 
                 62 
                 44 
                 33 
                 48 
                 93 
                 22 
                 29 
                 23 
                 98 
                 42 
               
               
                 28 
                 28 
                 33 
                 53 
                 64 
                 50 
                 36 
                 80 
                 61 
                 97 
                 70 
                 102 
                 57 
                 74 
               
               
                 29 
                 29 
                 44 
                 8 
                 31 
                 38 
                 24 
                 39 
                 100 
                 36 
                 11 
                 49 
                 68 
                 106 
               
               
                 30 
                 30 
                 22 
                 55 
                 69 
                 51 
                 86 
                 64 
                 50 
                 103 
                 18 
                 34 
                 109 
                 81 
               
               
                   
               
             
          
           
               
                   
                 Gr. Idx 
                   
                   
                   
               
               
                   
                 3RBs 
                 12RB 
                 15RB 
                 16RB 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 74 
                 51 
                 4 
                 6 
                 95 
                 140 
                 6 
                 102 
                 70 
               
               
                   
                 2 
                 9 
                 120 
                 44 
                 101 
                 71 
                 131 
                 76 
                 12 
                 108 
               
               
                   
                 3 
                 83 
                 13 
                 14 
                 17 
                 107 
                 77 
                 18 
                 114 
                 19 
               
               
                   
                 4 
                 18 
                 122 
                 87 
                 23 
                 83 
                 113 
                 25 
                 152 
                 120 
               
               
                   
                 5 
                 92 
                 23 
                 115 
                 29 
                 118 
                 148 
                 30 
                 158 
                 174 
               
               
                   
                 6 
                 27 
                 96 
                 131 
                 35 
                 154 
                 124 
                 37 
                 132 
                 101 
               
               
                   
                 7 
                 101 
                 124 
                 32 
                 40 
                 130 
                 160 
                 43 
                 139 
                 107 
               
               
                   
                 8 
                 36 
                 105 
                 8 
                 46 
                 136 
                 106 
                 49 
                 113 
                 145 
               
               
                   
                 9 
                 133 
                 110 
                 41 
                 52 
                 141 
                 171 
                 151 
                 103 
                 56 
               
               
                   
                 10 
                 45 
                 114 
                 91 
                 58 
                 147 
                 57 
                 62 
                 157 
                 189 
               
               
                   
                 11 
                 119 
                 3 
                 50 
                 64 
                 153 
                 4 
                 68 
                 67 
                 163 
               
               
                   
                 12 
                 54 
                 100 
                 123 
                 69 
                 159 
                 129 
                 74 
                 169 
                 10 
               
               
                   
                 13 
                 12 
                 58 
                 128 
                 75 
                 165 
                 135 
                 80 
                 176 
                 81 
               
               
                   
                 14 
                 63 
                 132 
                 7 
                 81 
                 21 
                 170 
                 86 
                 150 
                 182 
               
               
                   
                 15 
                 67 
                 137 
                 21 
                 86 
                 27 
                 176 
                 188 
                 93 
                 29 
               
               
                   
                 16 
                 2 
                 118 
                 71 
                 93 
                 152 
                 3 
                 3 
                 98 
                 162 
               
               
                   
                 17 
                 7 
                 76 
                 77 
                 158 
                 98 
                 9 
                 105 
                 41 
                 9 
               
               
                   
                 18 
                 11 
                 127 
                 81 
                 104 
                 14 
                 44 
                 111 
                 47 
                 15 
               
               
                   
                 19 
                 85 
                 39 
                 16 
                 20 
                 50 
                 110 
                 117 
                 22 
                 181 
               
               
                   
                 20 
                 136 
                 20 
                 89 
                 115 
                 26 
                 175 
                 28 
                 123 
                 124 
               
               
                   
                 21 
                 94 
                 48 
                 25 
                 121 
                 32 
                 122 
                 129 
                 34 
                 2 
               
               
                   
                 22 
                 6 
                 64 
                 52 
                 127 
                 38 
                 8 
                 135 
                 136 
                 59 
               
               
                   
                 23 
                 103 
                 34 
                 131 
                 133 
                 73 
                 132 
                 142 
                 78 
                 46 
               
               
                   
                 24 
                 38 
                 15 
                 73 
                 139 
                 49 
                 19 
                 148 
                 52 
                 84 
               
               
                   
                 25 
                 112 
                 66 
                 43 
                 144 
                 25 
                 55 
                 154 
                 59 
                 90 
               
               
                   
                 26 
                 47 
                 116 
                 24 
                 150 
                 61 
                 31 
                 33 
                 161 
                 17 
               
               
                   
                 27 
                 121 
                 75 
                 52 
                 156 
                 96 
                 155 
                 166 
                 39 
                 71 
               
               
                   
                 28 
                 56 
                 79 
                 126 
                 162 
                 72 
                 102 
                 173 
                 77 
                 45 
               
               
                   
                 29 
                 130 
                 95 
                 19 
                 78 
                 48 
                 108 
                 115 
                 179 
                 51 
               
               
                   
                 30 
                 65 
                 135 
                 134 
                 173 
                 54 
                 84 
                 185 
                 89 
                 121 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 26 
               
               
                   
               
               
                 Gr. Idx 
                   
                   
                   
                   
               
               
                 3RBs 
                 18RB 
                 20RB 
                 24RB 
                 25RB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 112 
                 7 
                 6 
                 8 
                 7 
                 167 
                 9 
                 151 
                 150 
                 9 
                 10 
                 156 
               
               
                 2 
                 119 
                 14 
                 84 
                 15 
                 135 
                 95 
                 19 
                 207 
                 18 
                 19 
                 165 
                 18 
               
               
                 3 
                 20 
                 126 
                 91 
                 23 
                 143 
                 103 
                 28 
                 27 
                 169 
                 28 
                 175 
                 126 
               
               
                 4 
                 133 
                 28 
                 168 
                 31 
                 150 
                 190 
                 36 
                 37 
                 178 
                 38 
                 184 
                 135 
               
               
                 5 
                 34 
                 175 
                 139 
                 39 
                 38 
                 158 
                 140 
                 45 
                 234 
                 194 
                 48 
                 145 
               
               
                 6 
                 41 
                 146 
                 40 
                 46 
                 126 
                 47 
                 55 
                 196 
                 149 
                 56 
                 203 
                 252 
               
               
                 7 
                 48 
                 153 
                 118 
                 54 
                 174 
                 173 
                 64 
                 205 
                 158 
                 66 
                 213 
                 212 
               
               
                 8 
                 54 
                 195 
                 139 
                 62 
                 181 
                 221 
                 73 
                 214 
                 262 
                 76 
                 222 
                 75 
               
               
                 9 
                 61 
                 202 
                 62 
                 69 
                 189 
                 70 
                 82 
                 223 
                 81 
                 85 
                 231 
                 183 
               
               
                 10 
                 68 
                 174 
                 209 
                 77 
                 197 
                 157 
                 91 
                 280 
                 92 
                 95 
                 241 
                 192 
               
               
                 11 
                 75 
                 74 
                 76 
                 85 
                 204 
                 5 
                 242 
                 195 
                 6 
                 104 
                 250 
                 251 
               
               
                 12 
                 187 
                 152 
                 81 
                 92 
                 13 
                 172 
                 109 
                 110 
                 204 
                 113 
                 260 
                 211 
               
               
                 13 
                 194 
                 36 
                 141 
                 220 
                 180 
                 101 
                 119 
                 213 
                 260 
                 123 
                 269 
                 25 
               
               
                 14 
                 95 
                 201 
                 25 
                 108 
                 107 
                 109 
                 128 
                 33 
                 270 
                 132 
                 230 
                 133 
               
               
                 15 
                 102 
                 208 
                 32 
                 116 
                 36 
                 235 
                 137 
                 136 
                 138 
                 288 
                 142 
                 44 
               
               
                 16 
                 109 
                 3 
                 179 
                 123 
                 203 
                 4 
                 146 
                 147 
                 4 
                 5 
                 151 
                 249 
               
               
                 17 
                 116 
                 10 
                 186 
                 131 
                 132 
                 130 
                 155 
                 13 
                 249 
                 161 
                 63 
                 160 
               
               
                 18 
                 17 
                 175 
                 70 
                 19 
                 59 
                 138 
                 164 
                 70 
                 23 
                 170 
                 24 
                 268 
               
               
                 19 
                 24 
                 59 
                 130 
                 27 
                 147 
                 146 
                 174 
                 173 
                 32 
                 180 
                 33 
                 179 
               
               
                 20 
                 136 
                 31 
                 137 
                 35 
                 154 
                 234 
                 41 
                 183 
                 277 
                 189 
                 43 
                 42 
               
               
                 21 
                 143 
                 37 
                 2 
                 162 
                 42 
                 82 
                 192 
                 50 
                 3 
                 198 
                 52 
                 101 
               
               
                 22 
                 150 
                 9 
                 149 
                 170 
                 169 
                 50 
                 201 
                 60 
                 202 
                 208 
                 62 
                 110 
               
               
                 23 
                 16 
                 30 
                 209 
                 58 
                 177 
                 18 
                 210 
                 69 
                 21 
                 218 
                 71 
                 22 
               
               
                 24 
                 163 
                 93 
                 23 
                 185 
                 65 
                 66 
                 219 
                 78 
                 125 
                 227 
                 80 
                 81 
               
               
                 25 
                 170 
                 65 
                 171 
                 193 
                 113 
                 192 
                 87 
                 228 
                 134 
                 237 
                 90 
                 41 
               
               
                 26 
                 177 
                 72 
                 176 
                 200 
                 81 
                 121 
                 96 
                 143 
                 49 
                 99 
                 245 
                 148 
               
               
                 27 
                 78 
                 183 
                 43 
                 208 
                 89 
                 49 
                 247 
                 246 
                 105 
                 255 
                 109 
                 254 
               
               
                 28 
                 85 
                 50 
                 138 
                 216 
                 96 
                 97 
                 256 
                 114 
                 67 
                 265 
                 118 
                 167 
               
               
                 29 
                 92 
                 197 
                 127 
                 224 
                 223 
                 104 
                 264 
                 76 
                 265 
                 274 
                 128 
                 275 
               
               
                 30 
                 46 
                 99 
                 204 
                 232 
                 231 
                 72 
                 274 
                 132 
                 180 
                 284 
                 283 
                 137 
               
               
                   
               
             
          
         
       
     
         [0117]    In another example, if the maximum number of sequences per each group is predetermined to 2, the grouping can be performed as shown in the following table 27. The table 27 is also the case when the base sequences are selected by actual cross correlation calculation. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 27 
               
               
                   
               
             
             
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
                 12RB 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 25 
                 2 
                 20 
                 2 
                 3 
                 25 
                 57 
                 4 
                 60 
                 79 
                 74 
                 51 
               
               
                 2 
                 2 
                 3 
                 4 
                 40 
                 33 
                 65 
                 28 
                 7 
                 71 
                 64 
                 45 
                 9 
                 120 
               
               
                 3 
                 3 
                 14 
                 6 
                 7 
                 21 
                 53 
                 9 
                 46 
                 10 
                 11 
                 39 
                 83 
                 13 
               
               
                 4 
                 4 
                 6 
                 47 
                 9 
                 66 
                 56 
                 41 
                 14 
                 85 
                 15 
                 71 
                 18 
                 122 
               
               
                 5 
                 5 
                 39 
                 39 
                 47 
                 54 
                 44 
                 50 
                 71 
                 44 
                 56 
                 75 
                 92 
                 23 
               
               
                 6 
                 6 
                 9 
                 31 
                 61 
                 14 
                 17 
                 84 
                 21 
                 92 
                 97 
                 50 
                 27 
                 96 
               
               
                 7 
                 7 
                 42 
                 33 
                 16 
                 28 
                 20 
                 87 
                 24 
                 51 
                 82 
                 63 
                 101 
                 124 
               
               
                 8 
                 8 
                 12 
                 30 
                 42 
                 54 
                 23 
                 5 
                 28 
                 99 
                 67 
                 86 
                 36 
                 105 
               
               
                 9 
                 9 
                 45 
                 17 
                 68 
                 21 
                 48 
                 85 
                 31 
                 74 
                 61 
                 89 
                 133 
                 110 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 5 
                 73 
                 29 
                 106 
                 70 
                 93 
                 112 
                 45 
                 114 
               
               
                 11 
                 11 
                 1 
                 21 
                 11 
                 25 
                 32 
                 2 
                 38 
                 102 
                 40 
                 78 
                 119 
                 3 
               
               
                 12 
                 12 
                 37 
                 23 
                 51 
                 63 
                 79 
                 64 
                 95 
                 77 
                 72 
                 44 
                 54 
                 100 
               
               
                 13 
                 13 
                 4 
                 5 
                 6 
                 30 
                 67 
                 37 
                 45 
                 9 
                 104 
                 47 
                 12 
                 58 
               
               
                 14 
                 14 
                 21 
                 7 
                 32 
                 22 
                 40 
                 58 
                 102 
                 84 
                 51 
                 6 
                 63 
                 132 
               
               
                 15 
                 15 
                 23 
                 58 
                 58 
                 34 
                 43 
                 61 
                 105 
                 16 
                 17 
                 111 
                 67 
                 137 
               
               
                 16 
                 16 
                 24 
                 1 
                 13 
                 65 
                 46 
                 28 
                 91 
                 2 
                 96 
                 2 
                 2 
                 118 
               
               
                 17 
                 17 
                 26 
                 52 
                 39 
                 49 
                 31 
                 49 
                 23 
                 59 
                 62 
                 107 
                 7 
                 76 
               
               
                 18 
                 18 
                 43 
                 54 
                 65 
                 41 
                 22 
                 52 
                 62 
                 98 
                 9 
                 66 
                 11 
                 127 
               
               
                 19 
                 19 
                 29 
                 36 
                 8 
                 20 
                 10 
                 25 
                 30 
                 12 
                 41 
                 24 
                 85 
                 39 
               
               
                 20 
                 20 
                 46 
                 38 
                 46 
                 60 
                 87 
                 57 
                 69 
                 5 
                 73 
                 35 
                 136 
                 20 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 66 
                 16 
                 60 
                 1 
                 37 
                 20 
                 1 
                 94 
                 48 
               
               
                 22 
                 22 
                 2 
                 42 
                 3 
                 50 
                 41 
                 78 
                 76 
                 49 
                 52 
                 24 
                 6 
                 64 
               
               
                 23 
                 23 
                 35 
                 29 
                 29 
                 17 
                 66 
                 55 
                 79 
                 8 
                 46 
                 27 
                 103 
                 34 
               
               
                 24 
                 24 
                 5 
                 26 
                 55 
                 43 
                 69 
                 2 
                 83 
                 56 
                 31 
                 12 
                 38 
                 15 
               
               
                 25 
                 25 
                 38 
                 28 
                 10 
                 57 
                 72 
                 27 
                 15 
                 65 
                 63 
                 46 
                 112 
                 66 
               
               
                 26 
                 26 
                 8 
                 20 
                 24 
                 17 
                 45 
                 75 
                 63 
                 54 
                 95 
                 57 
                 47 
                 116 
               
               
                 27 
                 27 
                 41 
                 22 
                 62 
                 44 
                 33 
                 48 
                 93 
                 22 
                 23 
                 98 
                 121 
                 75 
               
               
                 28 
                 28 
                 33 
                 53 
                 64 
                 50 
                 36 
                 80 
                 61 
                 97 
                 102 
                 57 
                 56 
                 79 
               
               
                 29 
                 29 
                 44 
                 8 
                 31 
                 38 
                 24 
                 39 
                 100 
                 36 
                 49 
                 68 
                 130 
                 95 
               
               
                 30 
                 30 
                 22 
                 55 
                 69 
                 51 
                 86 
                 64 
                 50 
                 103 
                 34 
                 109 
                 65 
                 135 
               
               
                   
               
             
          
           
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 15RB 
                 16RB 
                 18RB 
                 20RB 
                 24RB 
                 25RBs 
               
               
                   
               
             
          
           
               
                 1 
                 6 
                 95 
                 6 
                 102 
                 112 
                 7 
                 8 
                 7 
                 9 
                 151 
                 9 
                 10 
               
               
                 2 
                 101 
                 71 
                 76 
                 12 
                 119 
                 14 
                 15 
                 135 
                 19 
                 207 
                 19 
                 165 
               
               
                 3 
                 17 
                 107 
                 18 
                 114 
                 20 
                 126 
                 23 
                 143 
                 28 
                 27 
                 28 
                 175 
               
               
                 4 
                 23 
                 83 
                 25 
                 152 
                 133 
                 28 
                 31 
                 150 
                 36 
                 37 
                 38 
                 184 
               
               
                 5 
                 29 
                 118 
                 30 
                 158 
                 34 
                 175 
                 39 
                 38 
                 140 
                 45 
                 194 
                 48 
               
               
                 6 
                 35 
                 154 
                 37 
                 132 
                 41 
                 146 
                 46 
                 126 
                 55 
                 196 
                 56 
                 203 
               
               
                 7 
                 40 
                 130 
                 43 
                 139 
                 48 
                 153 
                 54 
                 174 
                 64 
                 205 
                 66 
                 213 
               
               
                 8 
                 46 
                 136 
                 49 
                 113 
                 54 
                 195 
                 62 
                 181 
                 73 
                 214 
                 76 
                 222 
               
               
                 9 
                 52 
                 141 
                 151 
                 103 
                 61 
                 202 
                 69 
                 189 
                 82 
                 223 
                 85 
                 231 
               
               
                 10 
                 58 
                 147 
                 62 
                 157 
                 68 
                 174 
                 77 
                 197 
                 91 
                 280 
                 95 
                 241 
               
               
                 11 
                 64 
                 153 
                 68 
                 67 
                 75 
                 74 
                 85 
                 204 
                 242 
                 195 
                 104 
                 250 
               
               
                 12 
                 69 
                 159 
                 74 
                 169 
                 187 
                 152 
                 92 
                 13 
                 109 
                 110 
                 113 
                 260 
               
               
                 13 
                 75 
                 165 
                 80 
                 176 
                 194 
                 36 
                 220 
                 180 
                 119 
                 213 
                 123 
                 269 
               
               
                 14 
                 81 
                 21 
                 86 
                 150 
                 95 
                 201 
                 108 
                 107 
                 128 
                 33 
                 132 
                 230 
               
               
                 15 
                 86 
                 27 
                 188 
                 93 
                 102 
                 208 
                 116 
                 36 
                 137 
                 136 
                 288 
                 142 
               
               
                 16 
                 93 
                 152 
                 3 
                 98 
                 109 
                 3 
                 123 
                 203 
                 146 
                 147 
                 5 
                 151 
               
               
                 17 
                 158 
                 98 
                 105 
                 41 
                 116 
                 10 
                 131 
                 132 
                 155 
                 13 
                 161 
                 63 
               
               
                 18 
                 104 
                 14 
                 111 
                 47 
                 17 
                 175 
                 19 
                 59 
                 164 
                 70 
                 170 
                 24 
               
               
                 19 
                 20 
                 50 
                 117 
                 22 
                 24 
                 59 
                 27 
                 147 
                 174 
                 173 
                 180 
                 33 
               
               
                 20 
                 115 
                 26 
                 28 
                 123 
                 136 
                 31 
                 35 
                 154 
                 41 
                 183 
                 189 
                 43 
               
               
                 21 
                 121 
                 32 
                 129 
                 34 
                 143 
                 37 
                 162 
                 42 
                 192 
                 50 
                 198 
                 52 
               
               
                 22 
                 127 
                 38 
                 135 
                 136 
                 150 
                 9 
                 170 
                 169 
                 201 
                 60 
                 208 
                 62 
               
               
                 23 
                 133 
                 73 
                 142 
                 78 
                 16 
                 30 
                 58 
                 177 
                 210 
                 69 
                 218 
                 71 
               
               
                 24 
                 139 
                 49 
                 148 
                 52 
                 163 
                 93 
                 185 
                 65 
                 219 
                 78 
                 227 
                 80 
               
               
                 25 
                 144 
                 25 
                 154 
                 59 
                 170 
                 65 
                 193 
                 113 
                 87 
                 228 
                 237 
                 90 
               
               
                 26 
                 150 
                 61 
                 33 
                 161 
                 177 
                 72 
                 200 
                 81 
                 96 
                 143 
                 99 
                 245 
               
               
                 27 
                 156 
                 96 
                 166 
                 39 
                 78 
                 183 
                 208 
                 89 
                 247 
                 246 
                 255 
                 109 
               
               
                 28 
                 162 
                 72 
                 173 
                 77 
                 85 
                 50 
                 216 
                 96 
                 256 
                 114 
                 265 
                 118 
               
               
                 29 
                 78 
                 48 
                 115 
                 179 
                 92 
                 197 
                 224 
                 223 
                 264 
                 76 
                 274 
                 128 
               
               
                 30 
                 173 
                 54 
                 185 
                 89 
                 46 
                 99 
                 232 
                 231 
                 274 
                 132 
                 284 
                 283 
               
               
                   
               
             
          
         
       
     
         [0118]    In another example, if the maximum number of sequences per each group is predetermined to 1, the grouping can be performed as shown in the following table 28. The table 28 is also the case when the base sequences are selected by actual cross correlation calculation. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 28 
               
               
                   
               
               
                 Gr. Idx 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 3RBs 
                 3RB 
                 4RB 
                 5RB 
                 6RB 
                 8RB 
                 9RB 
                 10RB 
                 12RB 
                 15RB 
                 16RB 
                 18RB 
                 20RB 
                 24RB 
                 25RBs 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1 
                 25 
                 2 
                 20 
                 3 
                 57 
                 60 
                 74 
                 6 
                 6 
                 112 
                 8 
                 9 
                 9 
               
               
                 2 
                 2 
                 3 
                 4 
                 40 
                 65 
                 7 
                 64 
                 9 
                 101 
                 76 
                 119 
                 15 
                 19 
                 19 
               
               
                 3 
                 3 
                 14 
                 6 
                 7 
                 53 
                 46 
                 11 
                 83 
                 17 
                 18 
                 20 
                 23 
                 28 
                 28 
               
               
                 4 
                 4 
                 6 
                 47 
                 9 
                 56 
                 14 
                 15 
                 18 
                 23 
                 25 
                 133 
                 31 
                 36 
                 38 
               
               
                 5 
                 5 
                 39 
                 39 
                 47 
                 44 
                 71 
                 56 
                 92 
                 29 
                 30 
                 34 
                 39 
                 140 
                 194 
               
               
                 6 
                 6 
                 9 
                 31 
                 61 
                 17 
                 21 
                 97 
                 27 
                 35 
                 37 
                 41 
                 46 
                 55 
                 56 
               
               
                 7 
                 7 
                 42 
                 33 
                 16 
                 20 
                 24 
                 82 
                 101 
                 40 
                 43 
                 48 
                 54 
                 64 
                 66 
               
               
                 8 
                 8 
                 12 
                 30 
                 42 
                 23 
                 28 
                 67 
                 36 
                 46 
                 49 
                 54 
                 62 
                 73 
                 76 
               
               
                 9 
                 9 
                 45 
                 17 
                 68 
                 48 
                 31 
                 61 
                 133 
                 52 
                 151 
                 61 
                 69 
                 82 
                 85 
               
               
                 10 
                 10 
                 15 
                 19 
                 23 
                 73 
                 106 
                 93 
                 45 
                 58 
                 62 
                 68 
                 77 
                 91 
                 95 
               
               
                 11 
                 11 
                 1 
                 21 
                 11 
                 32 
                 38 
                 40 
                 119 
                 64 
                 68 
                 75 
                 85 
                 242 
                 104 
               
               
                 12 
                 12 
                 37 
                 23 
                 51 
                 79 
                 95 
                 72 
                 54 
                 69 
                 74 
                 187 
                 92 
                 109 
                 113 
               
               
                 13 
                 13 
                 4 
                 5 
                 6 
                 67 
                 45 
                 104 
                 12 
                 75 
                 80 
                 194 
                 220 
                 119 
                 123 
               
               
                 14 
                 14 
                 21 
                 7 
                 32 
                 40 
                 102 
                 51 
                 63 
                 81 
                 86 
                 95 
                 108 
                 128 
                 132 
               
               
                 15 
                 15 
                 23 
                 58 
                 58 
                 43 
                 105 
                 17 
                 67 
                 86 
                 188 
                 102 
                 116 
                 137 
                 288 
               
               
                 16 
                 16 
                 24 
                 1 
                 13 
                 46 
                 91 
                 96 
                 2 
                 93 
                 3 
                 109 
                 123 
                 146 
                 5 
               
               
                 17 
                 17 
                 26 
                 52 
                 39 
                 31 
                 23 
                 62 
                 7 
                 158 
                 105 
                 116 
                 131 
                 155 
                 161 
               
               
                 18 
                 18 
                 43 
                 54 
                 65 
                 22 
                 62 
                 9 
                 11 
                 104 
                 111 
                 17 
                 19 
                 164 
                 170 
               
               
                 19 
                 19 
                 29 
                 36 
                 8 
                 10 
                 30 
                 41 
                 85 
                 20 
                 117 
                 24 
                 27 
                 174 
                 180 
               
               
                 20 
                 20 
                 46 
                 38 
                 46 
                 87 
                 69 
                 73 
                 136 
                 115 
                 28 
                 136 
                 35 
                 41 
                 189 
               
               
                 21 
                 21 
                 32 
                 40 
                 48 
                 16 
                 1 
                 20 
                 94 
                 121 
                 129 
                 143 
                 162 
                 192 
                 198 
               
               
                 22 
                 22 
                 2 
                 42 
                 3 
                 41 
                 76 
                 52 
                 6 
                 127 
                 135 
                 150 
                 170 
                 201 
                 208 
               
               
                 23 
                 23 
                 35 
                 29 
                 29 
                 66 
                 79 
                 46 
                 103 
                 133 
                 142 
                 16 
                 58 
                 210 
                 218 
               
               
                 24 
                 24 
                 5 
                 26 
                 55 
                 69 
                 83 
                 31 
                 38 
                 139 
                 148 
                 163 
                 185 
                 219 
                 227 
               
               
                 25 
                 25 
                 38 
                 28 
                 10 
                 72 
                 15 
                 63 
                 112 
                 144 
                 154 
                 170 
                 193 
                 87 
                 237 
               
               
                 26 
                 26 
                 8 
                 20 
                 24 
                 45 
                 63 
                 95 
                 47 
                 150 
                 33 
                 177 
                 200 
                 96 
                 99 
               
               
                 27 
                 27 
                 41 
                 22 
                 62 
                 33 
                 93 
                 23 
                 121 
                 156 
                 166 
                 78 
                 208 
                 247 
                 255 
               
               
                 28 
                 28 
                 33 
                 53 
                 64 
                 36 
                 61 
                 102 
                 56 
                 162 
                 173 
                 85 
                 216 
                 256 
                 265 
               
               
                 29 
                 29 
                 44 
                 8 
                 31 
                 24 
                 100 
                 49 
                 130 
                 78 
                 115 
                 92 
                 224 
                 264 
                 274 
               
               
                 30 
                 30 
                 22 
                 55 
                 69 
                 86 
                 50 
                 34 
                 65 
                 173 
                 185 
                 46 
                 232 
                 274 
                 284 
               
               
                   
               
             
          
         
       
     
         [0119]    For the above cases, the tables can be reorganized according to the allocated number of sequence per each group and each length. 
         [0120]    For another example of this invention, the above tables can be extended to 100 RB length, and following tables show this example. In this example, the maximum number of the root index number (v) for 5 RB length or less is set to 1, and maximum number of the root index number (v) for the length longer than 5 RB is set to 2. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 29 
               
               
                   
                   
               
             
             
               
                   
                 RB 
                 3 
                 4 
                 5 
                 6 
                 8 
                 9 
                 10 
                 12 
                 15 
               
               
                   
                 Nzc 
                 31 
                 47 
                 59 
                 71 
                 89 
                 107 
                 113 
                 139 
                 179 
               
               
                   
                 Max 
                 1 
                 1 
                 1 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                   
                 root 
               
               
                   
                 per 
               
               
                   
                 RB 
               
               
                   
                   
               
             
          
           
               
                 Gr. 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Idx 
                 v 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
               
                 0 
                   
                 0 
                 2 
                 2 
                 2 
                 3 
                 3 
                 2 
                 3 
                 4 
                 4 
                 3 
                 4 
                 5 
                 6 
                 5 
               
               
                 1 
                   
                 1 
                 3 
                 4 
                 5 
                 4 
                 6 
                 5 
                 7 
                 6 
                 7 
                 8 
                 9 
                 8 
                 12 
                 11 
               
               
                 2 
                   
                 2 
                 5 
                 6 
                 7 
                 6 
                 9 
                 8 
                 10 
                 11 
                 11 
                 10 
                 13 
                 14 
                 17 
                 18 
               
               
                 3 
                   
                 3 
                 6 
                 8 
                 9 
                 10 
                 11 
                 12 
                 14 
                 13 
                 15 
                 14 
                 18 
                 17 
                 23 
                 24 
               
               
                 4 
                   
                 4 
                 8 
                 10 
                 11 
                 12 
                 14 
                 15 
                 17 
                 18 
                 18 
                 19 
                 22 
                 23 
                 29 
                 28 
               
               
                 5 
                   
                 5 
                 9 
                 11 
                 14 
                 13 
                 17 
                 18 
                 21 
                 20 
                 22 
                 21 
                 27 
                 26 
                 35 
                 34 
               
               
                 6 
                   
                 6 
                 11 
                 13 
                 16 
                 17 
                 20 
                 21 
                 24 
                 25 
                 26 
                 25 
                 31 
                 32 
                 40 
                 41 
               
               
                 7 
                   
                 7 
                 12 
                 15 
                 18 
                 19 
                 23 
                 22 
                 28 
                 27 
                 29 
                 30 
                 36 
                 35 
                 46 
                 47 
               
               
                 8 
                   
                 8 
                 14 
                 17 
                 21 
                 20 
                 26 
                 25 
                 31 
                 32 
                 33 
                 32 
                 40 
                 41 
                 52 
                 51 
               
               
                 9 
                   
                 9 
                 15 
                 19 
                 23 
                 22 
                 29 
                 28 
                 35 
                 34 
                 36 
                 37 
                 45 
                 44 
                 58 
                 57 
               
               
                 10 
                   
                 10 
                 17 
                 21 
                 25 
                 26 
                 32 
                 31 
                 38 
                 37 
                 40 
                 41 
                 49 
                 50 
                 64 
                 63 
               
               
                 11 
                   
                 11 
                 18 
                 23 
                 27 
                 28 
                 34 
                 35 
                 41 
                 42 
                 44 
                 43 
                 54 
                 53 
                 69 
                 70 
               
               
                 12 
                   
                 12 
                 20 
                 25 
                 30 
                 29 
                 37 
                 38 
                 45 
                 44 
                 47 
                 48 
                 58 
                 59 
                 75 
                 76 
               
               
                 13 
                   
                 13 
                 21 
                 27 
                 32 
                 33 
                 40 
                 41 
                 48 
                 49 
                 51 
                 52 
                 63 
                 62 
                 81 
                 80 
               
               
                 14 
                   
                 14 
                 23 
                 29 
                 34 
                 35 
                 43 
                 44 
                 52 
                 51 
                 55 
                 54 
                 67 
                 68 
                 87 
                 86 
               
               
                 15 
                   
                 15 
                 24 
                 30 
                 37 
                 36 
                 46 
                 45 
                 55 
                 56 
                 58 
                 59 
                 72 
                 71 
                 92 
                 93 
               
               
                 16 
                   
                 16 
                 26 
                 32 
                 39 
                 38 
                 49 
                 48 
                 59 
                 58 
                 62 
                 61 
                 76 
                 77 
                 98 
                 99 
               
               
                 17 
                   
                 17 
                 27 
                 34 
                 41 
                 42 
                 52 
                 51 
                 62 
                 63 
                 66 
                 65 
                 81 
                 80 
                 104 
                 103 
               
               
                 18 
                   
                 18 
                 29 
                 36 
                 44 
                 43 
                 55 
                 54 
                 66 
                 65 
                 69 
                 70 
                 85 
                 86 
                 110 
                 109 
               
               
                 19 
                   
                 19 
                 30 
                 38 
                 46 
                 45 
                 57 
                 58 
                 69 
                 70 
                 73 
                 72 
                 90 
                 89 
                 115 
                 116 
               
               
                 20 
                   
                 20 
                 32 
                 40 
                 48 
                 49 
                 60 
                 61 
                 72 
                 73 
                 77 
                 76 
                 94 
                 95 
                 121 
                 122 
               
               
                 21 
                   
                 21 
                 33 
                 42 
                 50 
                 51 
                 63 
                 64 
                 76 
                 75 
                 80 
                 81 
                 99 
                 98 
                 127 
                 128 
               
               
                 22 
                   
                 22 
                 35 
                 44 
                 53 
                 52 
                 66 
                 67 
                 79 
                 80 
                 84 
                 83 
                 103 
                 104 
                 133 
                 132 
               
               
                 23 
                   
                 23 
                 36 
                 46 
                 55 
                 54 
                 69 
                 68 
                 83 
                 82 
                 87 
                 88 
                 108 
                 107 
                 139 
                 138 
               
               
                 24 
                   
                 24 
                 38 
                 48 
                 57 
                 58 
                 72 
                 71 
                 86 
                 87 
                 91 
                 92 
                 112 
                 113 
                 144 
                 145 
               
               
                 25 
                   
                 25 
                 39 
                 49 
                 60 
                 59 
                 75 
                 74 
                 90 
                 89 
                 95 
                 94 
                 117 
                 116 
                 150 
                 151 
               
               
                 26 
                   
                 26 
                 41 
                 51 
                 62 
                 61 
                 78 
                 77 
                 93 
                 94 
                 98 
                 99 
                 121 
                 122 
                 156 
                 155 
               
               
                 27 
                   
                 27 
                 42 
                 53 
                 64 
                 65 
                 80 
                 81 
                 97 
                 96 
                 102 
                 103 
                 126 
                 125 
                 162 
                 161 
               
               
                 28 
                   
                 28 
                 44 
                 55 
                 66 
                 67 
                 83 
                 84 
                 100 
                 101 
                 106 
                 105 
                 130 
                 131 
                 167 
                 168 
               
               
                 29 
                   
                 29 
                 45 
                 57 
                 69 
                 68 
                 86 
                 87 
                 104 
                 103 
                 109 
                 110 
                 135 
                 134 
                 173 
                 174 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 30 
               
               
                   
                   
               
             
             
               
                   
                 RB 
                 16 
                 18 
                 20 
                 24 
                 25 
                 27 
                 30 
                 32 
               
               
                   
                 Nzc 
                 191 
                 211 
                 239 
                 283 
                 293 
                 317 
                 359 
                 383 
               
               
                   
                 Max 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                   
                 root 
               
               
                   
                 per 
               
               
                   
                 RB 
               
               
                   
                   
               
             
          
           
               
                 Gr. 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Idx 
                 v 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
               
                 0 
                   
                 6 
                 7 
                 7 
                 6 
                 8 
                 7 
                 9 
                 10 
                 9 
                 10 
                 10 
                 11 
                 12 
                 11 
                 12 
                 13 
               
               
                 1 
                   
                 12 
                 13 
                 14 
                 13 
                 15 
                 16 
                 18 
                 19 
                 19 
                 18 
                 20 
                 21 
                 23 
                 24 
                 25 
                 24 
               
               
                 2 
                   
                 18 
                 19 
                 20 
                 21 
                 23 
                 24 
                 27 
                 28 
                 28 
                 29 
                 31 
                 30 
                 35 
                 34 
                 37 
                 38 
               
               
                 3 
                   
                 25 
                 24 
                 27 
                 28 
                 31 
                 30 
                 37 
                 36 
                 38 
                 37 
                 41 
                 40 
                 46 
                 47 
                 49 
                 50 
               
               
                 4 
                   
                 31 
                 30 
                 34 
                 35 
                 39 
                 38 
                 46 
                 45 
                 47 
                 48 
                 51 
                 52 
                 58 
                 57 
                 62 
                 61 
               
               
                 5 
                   
                 37 
                 36 
                 41 
                 40 
                 46 
                 47 
                 55 
                 54 
                 57 
                 56 
                 61 
                 62 
                 69 
                 70 
                 74 
                 75 
               
               
                 6 
                   
                 43 
                 44 
                 48 
                 47 
                 54 
                 53 
                 64 
                 63 
                 66 
                 67 
                 72 
                 71 
                 81 
                 82 
                 86 
                 87 
               
               
                 7 
                   
                 49 
                 50 
                 54 
                 55 
                 62 
                 61 
                 73 
                 74 
                 76 
                 75 
                 82 
                 81 
                 93 
                 92 
                 99 
                 98 
               
               
                 8 
                   
                 55 
                 56 
                 61 
                 62 
                 69 
                 70 
                 82 
                 83 
                 85 
                 86 
                 92 
                 93 
                 104 
                 105 
                 111 
                 112 
               
               
                 9 
                   
                 62 
                 61 
                 68 
                 69 
                 77 
                 78 
                 91 
                 92 
                 95 
                 94 
                 102 
                 103 
                 116 
                 115 
                 124 
                 123 
               
               
                 10 
                   
                 68 
                 67 
                 75 
                 74 
                 85 
                 84 
                 100 
                 101 
                 104 
                 103 
                 112 
                 113 
                 127 
                 128 
                 136 
                 135 
               
               
                 11 
                   
                 74 
                 73 
                 82 
                 81 
                 93 
                 92 
                 110 
                 109 
                 113 
                 114 
                 123 
                 122 
                 139 
                 138 
                 148 
                 149 
               
               
                 12 
                   
                 80 
                 81 
                 88 
                 89 
                 100 
                 101 
                 119 
                 118 
                 123 
                 122 
                 133 
                 132 
                 151 
                 150 
                 161 
                 160 
               
               
                 13 
                   
                 86 
                 87 
                 95 
                 96 
                 108 
                 107 
                 128 
                 127 
                 132 
                 133 
                 143 
                 144 
                 162 
                 163 
                 173 
                 172 
               
               
                 14 
                   
                 92 
                 93 
                 102 
                 103 
                 116 
                 115 
                 137 
                 136 
                 142 
                 141 
                 153 
                 154 
                 174 
                 173 
                 185 
                 186 
               
               
                 15 
                   
                 99 
                 98 
                 109 
                 108 
                 123 
                 124 
                 146 
                 147 
                 151 
                 152 
                 164 
                 163 
                 185 
                 186 
                 198 
                 197 
               
               
                 16 
                   
                 105 
                 104 
                 116 
                 115 
                 131 
                 132 
                 155 
                 156 
                 161 
                 160 
                 174 
                 173 
                 197 
                 196 
                 210 
                 211 
               
               
                 17 
                   
                 111 
                 110 
                 123 
                 122 
                 139 
                 138 
                 164 
                 165 
                 170 
                 171 
                 184 
                 185 
                 208 
                 209 
                 222 
                 223 
               
               
                 18 
                   
                 117 
                 118 
                 129 
                 130 
                 146 
                 147 
                 173 
                 174 
                 180 
                 179 
                 194 
                 195 
                 220 
                 221 
                 235 
                 234 
               
               
                 19 
                   
                 123 
                 124 
                 136 
                 137 
                 154 
                 155 
                 183 
                 182 
                 189 
                 190 
                 205 
                 204 
                 232 
                 231 
                 247 
                 248 
               
               
                 20 
                   
                 129 
                 130 
                 143 
                 142 
                 162 
                 161 
                 192 
                 191 
                 198 
                 199 
                 215 
                 214 
                 243 
                 244 
                 259 
                 260 
               
               
                 21 
                   
                 136 
                 135 
                 150 
                 149 
                 170 
                 169 
                 201 
                 200 
                 208 
                 207 
                 225 
                 224 
                 255 
                 254 
                 272 
                 271 
               
               
                 22 
                   
                 142 
                 141 
                 157 
                 156 
                 177 
                 178 
                 210 
                 209 
                 217 
                 218 
                 235 
                 236 
                 266 
                 267 
                 284 
                 285 
               
               
                 23 
                   
                 148 
                 147 
                 163 
                 164 
                 185 
                 186 
                 219 
                 220 
                 227 
                 226 
                 245 
                 246 
                 278 
                 277 
                 297 
                 296 
               
               
                 24 
                   
                 154 
                 155 
                 170 
                 171 
                 193 
                 192 
                 228 
                 229 
                 236 
                 237 
                 256 
                 255 
                 290 
                 289 
                 309 
                 308 
               
               
                 25 
                   
                 160 
                 161 
                 177 
                 176 
                 200 
                 201 
                 237 
                 238 
                 246 
                 245 
                 266 
                 265 
                 301 
                 302 
                 321 
                 322 
               
               
                 26 
                   
                 166 
                 167 
                 184 
                 183 
                 208 
                 209 
                 246 
                 247 
                 255 
                 256 
                 276 
                 277 
                 313 
                 312 
                 334 
                 333 
               
               
                 27 
                   
                 173 
                 172 
                 191 
                 190 
                 216 
                 215 
                 256 
                 255 
                 265 
                 264 
                 286 
                 287 
                 324 
                 325 
                 346 
                 345 
               
               
                 28 
                   
                 179 
                 178 
                 197 
                 198 
                 224 
                 223 
                 265 
                 264 
                 274 
                 275 
                 297 
                 296 
                 336 
                 335 
                 358 
                 359 
               
               
                 29 
                   
                 185 
                 184 
                 204 
                 205 
                 231 
                 232 
                 274 
                 273 
                 284 
                 283 
                 307 
                 306 
                 347 
                 348 
                 371 
                 370 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 31 
               
               
                   
               
             
             
               
                 1 
                 RB 
                 36 
                 40 
                 45 
                 48 
                 50 
                 54 
                 60 
                 64 
               
               
                 2 
                 Nzc 
                 431 
                 479 
                 523 
                 571 
                 599 
                 647 
                 719 
                 761 
               
               
                   
                 Max 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                   
                 root 
               
               
                   
                 per 
               
               
                   
                 RB 
               
               
                   
               
             
          
           
               
                 Gr. 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Idx 
                 v 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
               
                 0 
                   
                 14 
                 13 
                 15 
                 16 
                 17 
                 16 
                 18 
                 19 
                 19 
                 20 
                 21 
                 20 
                 23 
                 24 
                 25 
                 24 
               
               
                 1 
                   
                 28 
                 27 
                 31 
                 30 
                 34 
                 33 
                 37 
                 36 
                 39 
                 38 
                 42 
                 41 
                 46 
                 47 
                 49 
                 50 
               
               
                 2 
                   
                 42 
                 41 
                 46 
                 47 
                 51 
                 50 
                 55 
                 56 
                 58 
                 57 
                 63 
                 62 
                 70 
                 69 
                 74 
                 73 
               
               
                 3 
                   
                 56 
                 55 
                 62 
                 61 
                 67 
                 68 
                 74 
                 73 
                 77 
                 78 
                 83 
                 84 
                 93 
                 92 
                 98 
                 99 
               
               
                 4 
                   
                 70 
                 69 
                 77 
                 78 
                 84 
                 85 
                 92 
                 93 
                 97 
                 96 
                 104 
                 105 
                 116 
                 115 
                 123 
                 122 
               
               
                 5 
                   
                 83 
                 84 
                 93 
                 92 
                 101 
                 102 
                 111 
                 110 
                 116 
                 115 
                 125 
                 126 
                 139 
                 140 
                 147 
                 148 
               
               
                 6 
                   
                 97 
                 98 
                 108 
                 109 
                 118 
                 119 
                 129 
                 128 
                 135 
                 136 
                 146 
                 147 
                 162 
                 163 
                 172 
                 171 
               
               
                 7 
                   
                 111 
                 112 
                 124 
                 123 
                 135 
                 134 
                 147 
                 148 
                 155 
                 154 
                 167 
                 166 
                 186 
                 185 
                 196 
                 197 
               
               
                 8 
                   
                 125 
                 126 
                 139 
                 140 
                 152 
                 151 
                 166 
                 165 
                 174 
                 173 
                 188 
                 187 
                 209 
                 208 
                 221 
                 220 
               
               
                 9 
                   
                 139 
                 140 
                 155 
                 154 
                 169 
                 168 
                 184 
                 185 
                 193 
                 194 
                 209 
                 208 
                 232 
                 231 
                 245 
                 246 
               
               
                 10 
                   
                 153 
                 152 
                 170 
                 169 
                 186 
                 185 
                 203 
                 202 
                 213 
                 212 
                 230 
                 229 
                 255 
                 256 
                 270 
                 271 
               
               
                 11 
                   
                 167 
                 166 
                 185 
                 186 
                 202 
                 203 
                 221 
                 222 
                 232 
                 231 
                 250 
                 251 
                 278 
                 279 
                 295 
                 294 
               
               
                 12 
                   
                 181 
                 180 
                 201 
                 200 
                 219 
                 220 
                 239 
                 240 
                 251 
                 252 
                 271 
                 272 
                 302 
                 301 
                 319 
                 320 
               
               
                 13 
                   
                 195 
                 194 
                 216 
                 217 
                 236 
                 237 
                 258 
                 257 
                 271 
                 270 
                 292 
                 293 
                 325 
                 324 
                 344 
                 343 
               
               
                 14 
                   
                 209 
                 208 
                 232 
                 231 
                 253 
                 254 
                 276 
                 277 
                 290 
                 289 
                 313 
                 314 
                 348 
                 347 
                 368 
                 369 
               
               
                 15 
                   
                 222 
                 223 
                 247 
                 248 
                 270 
                 269 
                 295 
                 294 
                 309 
                 310 
                 334 
                 333 
                 371 
                 372 
                 393 
                 392 
               
               
                 16 
                   
                 236 
                 237 
                 263 
                 262 
                 287 
                 286 
                 313 
                 314 
                 328 
                 329 
                 355 
                 354 
                 394 
                 395 
                 417 
                 418 
               
               
                 17 
                   
                 250 
                 251 
                 278 
                 279 
                 304 
                 303 
                 332 
                 331 
                 348 
                 347 
                 376 
                 375 
                 417 
                 418 
                 442 
                 441 
               
               
                 18 
                   
                 264 
                 265 
                 294 
                 293 
                 321 
                 320 
                 350 
                 349 
                 367 
                 368 
                 397 
                 396 
                 441 
                 440 
                 466 
                 467 
               
               
                 19 
                   
                 278 
                 279 
                 309 
                 310 
                 337 
                 338 
                 368 
                 369 
                 386 
                 387 
                 417 
                 418 
                 464 
                 463 
                 491 
                 490 
               
               
                 20 
                   
                 292 
                 291 
                 324 
                 325 
                 354 
                 355 
                 387 
                 386 
                 406 
                 405 
                 438 
                 439 
                 487 
                 488 
                 516 
                 515 
               
               
                 21 
                   
                 306 
                 305 
                 340 
                 339 
                 371 
                 372 
                 405 
                 406 
                 425 
                 426 
                 459 
                 460 
                 510 
                 511 
                 540 
                 541 
               
               
                 22 
                   
                 320 
                 319 
                 355 
                 356 
                 388 
                 389 
                 424 
                 423 
                 444 
                 445 
                 480 
                 481 
                 533 
                 534 
                 565 
                 564 
               
               
                 23 
                   
                 334 
                 333 
                 371 
                 370 
                 405 
                 404 
                 442 
                 443 
                 464 
                 463 
                 501 
                 500 
                 557 
                 556 
                 589 
                 590 
               
               
                 24 
                   
                 348 
                 347 
                 386 
                 387 
                 422 
                 421 
                 460 
                 461 
                 483 
                 484 
                 522 
                 521 
                 580 
                 579 
                 614 
                 613 
               
               
                 25 
                   
                 361 
                 362 
                 402 
                 401 
                 439 
                 438 
                 479 
                 478 
                 502 
                 503 
                 543 
                 542 
                 603 
                 604 
                 638 
                 639 
               
               
                 26 
                   
                 375 
                 376 
                 417 
                 418 
                 456 
                 455 
                 497 
                 498 
                 522 
                 521 
                 564 
                 563 
                 626 
                 627 
                 663 
                 662 
               
               
                 27 
                   
                 389 
                 390 
                 433 
                 432 
                 472 
                 473 
                 516 
                 515 
                 541 
                 542 
                 584 
                 585 
                 649 
                 650 
                 687 
                 688 
               
               
                 28 
                   
                 403 
                 404 
                 448 
                 449 
                 489 
                 490 
                 534 
                 535 
                 560 
                 561 
                 605 
                 606 
                 673 
                 672 
                 712 
                 711 
               
               
                 29 
                   
                 417 
                 418 
                 464 
                 463 
                 506 
                 507 
                 553 
                 552 
                 580 
                 579 
                 626 
                 627 
                 696 
                 695 
                 736 
                 737 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 32 
               
               
                   
               
             
             
               
                 1 
                 RB 
                 72 
                 75 
                 80 
                 81 
                 90 
                 96 
                 100 
               
               
                 2 
                 Nzc 
                 863 
                 887 
                 953 
                 971 
                 1069 
                 1151 
                 1193 
               
               
                   
                 Max 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                   
                 root 
               
               
                   
                 per 
               
               
                   
                 RB 
               
               
                   
               
             
          
           
               
                 Gr. 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Idx 
                 v 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
               
                 0 
                   
                 28 
                 27 
                 29 
                 28 
                 31 
                 30 
                 31 
                 32 
                 34 
                 35 
                 37 
                 38 
                 38 
                 39 
               
               
                 1 
                   
                 56 
                 55 
                 57 
                 58 
                 61 
                 62 
                 63 
                 62 
                 69 
                 68 
                 74 
                 75 
                 77 
                 76 
               
               
                 2 
                   
                 84 
                 83 
                 86 
                 85 
                 92 
                 93 
                 94 
                 93 
                 103 
                 104 
                 111 
                 112 
                 115 
                 116 
               
               
                 3 
                   
                 111 
                 112 
                 114 
                 115 
                 123 
                 122 
                 125 
                 126 
                 138 
                 137 
                 149 
                 148 
                 154 
                 153 
               
               
                 4 
                   
                 139 
                 140 
                 143 
                 144 
                 154 
                 153 
                 157 
                 156 
                 172 
                 173 
                 186 
                 185 
                 192 
                 193 
               
               
                 5 
                   
                 167 
                 168 
                 172 
                 171 
                 184 
                 185 
                 188 
                 187 
                 207 
                 206 
                 223 
                 222 
                 231 
                 230 
               
               
                 6 
                   
                 195 
                 194 
                 200 
                 201 
                 215 
                 216 
                 219 
                 220 
                 241 
                 242 
                 260 
                 259 
                 269 
                 270 
               
               
                 7 
                   
                 223 
                 222 
                 229 
                 228 
                 246 
                 245 
                 251 
                 250 
                 276 
                 275 
                 297 
                 298 
                 308 
                 307 
               
               
                 8 
                   
                 251 
                 250 
                 258 
                 257 
                 277 
                 276 
                 282 
                 281 
                 310 
                 311 
                 334 
                 335 
                 346 
                 347 
               
               
                 9 
                   
                 278 
                 279 
                 286 
                 287 
                 307 
                 308 
                 313 
                 314 
                 345 
                 344 
                 371 
                 372 
                 385 
                 384 
               
               
                 10 
                   
                 306 
                 307 
                 315 
                 314 
                 338 
                 339 
                 345 
                 344 
                 379 
                 380 
                 408 
                 409 
                 423 
                 424 
               
               
                 11 
                   
                 334 
                 335 
                 343 
                 344 
                 369 
                 368 
                 376 
                 375 
                 414 
                 413 
                 446 
                 445 
                 462 
                 461 
               
               
                 12 
                   
                 362 
                 361 
                 372 
                 371 
                 400 
                 399 
                 407 
                 408 
                 448 
                 449 
                 483 
                 482 
                 500 
                 501 
               
               
                 13 
                   
                 390 
                 389 
                 401 
                 400 
                 430 
                 431 
                 439 
                 438 
                 483 
                 482 
                 520 
                 519 
                 539 
                 538 
               
               
                 14 
                   
                 418 
                 417 
                 429 
                 430 
                 461 
                 462 
                 470 
                 469 
                 517 
                 518 
                 557 
                 556 
                 577 
                 578 
               
               
                 15 
                   
                 445 
                 446 
                 458 
                 457 
                 492 
                 491 
                 501 
                 502 
                 552 
                 551 
                 594 
                 595 
                 616 
                 615 
               
               
                 16 
                   
                 473 
                 474 
                 486 
                 487 
                 523 
                 522 
                 532 
                 533 
                 586 
                 587 
                 631 
                 632 
                 654 
                 655 
               
               
                 17 
                   
                 501 
                 502 
                 515 
                 516 
                 553 
                 554 
                 564 
                 563 
                 621 
                 620 
                 668 
                 669 
                 693 
                 692 
               
               
                 18 
                   
                 529 
                 528 
                 544 
                 543 
                 584 
                 585 
                 595 
                 596 
                 655 
                 656 
                 705 
                 706 
                 731 
                 732 
               
               
                 19 
                   
                 557 
                 556 
                 572 
                 573 
                 615 
                 614 
                 626 
                 627 
                 690 
                 689 
                 743 
                 742 
                 770 
                 769 
               
               
                 20 
                   
                 585 
                 584 
                 601 
                 600 
                 646 
                 645 
                 658 
                 657 
                 724 
                 725 
                 780 
                 779 
                 808 
                 809 
               
               
                 21 
                   
                 612 
                 613 
                 629 
                 630 
                 676 
                 677 
                 689 
                 690 
                 759 
                 758 
                 817 
                 816 
                 847 
                 846 
               
               
                 22 
                   
                 640 
                 641 
                 658 
                 659 
                 707 
                 708 
                 720 
                 721 
                 793 
                 794 
                 854 
                 853 
                 885 
                 886 
               
               
                 23 
                   
                 668 
                 669 
                 687 
                 686 
                 738 
                 737 
                 752 
                 751 
                 828 
                 827 
                 891 
                 892 
                 924 
                 923 
               
               
                 24 
                   
                 696 
                 695 
                 715 
                 716 
                 769 
                 768 
                 783 
                 784 
                 862 
                 863 
                 928 
                 929 
                 962 
                 963 
               
               
                 25 
                   
                 724 
                 723 
                 744 
                 743 
                 799 
                 800 
                 814 
                 815 
                 897 
                 896 
                 965 
                 966 
                 1001 
                 1000 
               
               
                 26 
                   
                 752 
                 751 
                 773 
                 772 
                 830 
                 831 
                 846 
                 845 
                 931 
                 932 
                 1002 
                 1003 
                 1039 
                 1040 
               
               
                 27 
                   
                 779 
                 780 
                 801 
                 802 
                 861 
                 860 
                 877 
                 878 
                 966 
                 965 
                 1040 
                 1039 
                 1078 
                 1077 
               
               
                 28 
                   
                 807 
                 808 
                 830 
                 829 
                 892 
                 891 
                 908 
                 909 
                 1000 
                 1001 
                 1077 
                 1076 
                 1116 
                 1117 
               
               
                 29 
                   
                 835 
                 836 
                 858 
                 859 
                 922 
                 923 
                 940 
                 939 
                 1035 
                 1034 
                 1114 
                 1113 
                 1155 
                 1154 
               
               
                   
               
             
          
         
       
     
         [0121]    Based on these concepts, the present invention provides a method for generating reference signal sequence using ZC sequence as follows. 
         [0122]    To generate reference signal sequence, one embodiment of the present invention defines a specific base sequence for allying cyclic shift. In this embodiment, the base sequence is defined using ZC sequence with certain root index (hereinafter “q”). And, the specific base sequence is selected from the base sequence groups, and each of the base sequence group contains base sequences having a high cross correlation relation as stated above. So, if one wants to select the specific base sequence with index of “q”, the “q” should be selected considering the group index (hereinafter “u”) and the base sequence number index within each group (hereinafter “v”). That is, “q” should be a function of “u” and “v”. 
         [0123]    And, after the specific base sequence with root index “q” is selected, then the cyclic shift corresponding to various cyclic shift values can be applied to the selected base sequence. 
         [0124]    If the relation between the “q”, “u” and “v” is more specifically considered, “q” can be acquired by the following equations. The following equations 17 and 18 are for selecting the index “q” to meet the condition that the term (s 1 /N 1 −s 2 /N 2 ) becomes close to zero. 
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
                                 1 
                               
                               2 
                             
                             ) 
                           
                         
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     round 
                                      
                                     
                                       ( 
                                       y 
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
                             + 
                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           N 
                           
                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     17 
                   
                   ] 
                 
               
             
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
                                 1 
                               
                               2 
                             
                             ) 
                           
                         
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     floor 
                                      
                                     
                                       ( 
                                       
                                         y 
                                         + 
                                         0.5 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
                             + 
                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           N 
                           
                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
         [0125]    Here, N zc   RS  is the target ZC sequence generation length used in generating the q-th root ZC sequence, and N zc   RS  is given by the largest prime number which is less than the corresponding reference signal sequence size. That is, the base sequence is generated by cyclic extension method. 
         [0126]    And, N reference,zc   RS  is the length given by the largest prime number which is less than the reference sequence size, for example, 3 RB length. If the grouping is based on the 3 RB length, then N reference,zc   RS  is 31. The “round (z)” is a function of rounding off to a nearest integer nearest to z, and the “floor (z)” is a function of making a greatest integer not greater than z. 
         [0127]    And, according to another embodiment of this invention, if the ZC sequence is generated based on the truncation method, then N zc   RS  can be given by the smallest prime number which is greater than the corresponding reference signal sequence size. And, in this case, N reference,zc   RS  can be the length given by the smallest prime number which is greater than the reference sequence size, for example, 3 RB length. If the grouping is based on the 3 RB length, then N reference,zc   RS  can be 37. 
         [0128]    And, according to equations 17 and 18, “m”-th element of the “q”-th ZC sequence (x q (m)) can be expressed as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         q 
                       
                        
                       
                         ( 
                         m 
                         ) 
                       
                     
                     = 
                     
                        
                       
                         
                           - 
                           j 
                         
                          
                         
                           
                             π 
                              
                             
                                 
                             
                              
                             qm 
                              
                             
                               ( 
                               
                                 m 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             N 
                             ZC 
                             RS 
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     0 
                     ≤ 
                     m 
                     ≤ 
                     
                       
                         N 
                         ZC 
                         RS 
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     19 
                   
                   ] 
                 
               
             
           
         
       
     
         [0129]    Because “round (y)” and “floor (y+0.5)” are actually equivalent, the equations 17 and 18 have the same meaning. In the equations 17 and 18, the term (−1) floor(round(y)-y)  means that if “y” has 0.5 or greater value in its decimal place, (−1) floor(round(y)-y)  can be calculated as “1”, and if “y” has the value less than 0.5 in its decimal place, (−1) floor(round(y)-y)  can be calculated as “−1”. So, (−1) floor(round(y)-y) can be replaced with (− 1) floor(round(y)-y)  or any other equivalent terms having the same meaning. 
         [0130]    In the above examples, when the grouping is performed for the length greater than the 3 RB length based on the 3 RB length, and when the ZC sequence is generated based on the cyclic extension method, N reference,zc   RS  can be 31. Also, when the ZC sequence is generated based on the truncation method, N reference,zc   RS  can be 37. And, when the grouping is performed for the length greater than the 4 RB length based on the 4 RB length, and when the ZC sequence is generated based on the cyclic extension method, N reference,zc   RS  can be 47. Also, when the ZC sequence is generated based on the truncation method, N reference,zc   RS  can be 49. And, this can be easily employed to other length based grouping. 
         [0131]    Above mentioned tables can be acquired by the equations 17 and 18. The following examples are part of selecting root index according to the equations 17 and 18. 
         [0132]    First, if the N reference,zc =31, the method for selecting first group (“u”=0) when 1) Nzc=47, 2) Nzc=71 3) Nzc=211 is as follows. In the following examples, the equation 18 is used. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       
                         reference 
                         , 
                         zc 
                       
                     
                     = 
                     31 
                   
                   , 
                   
                     
                       N 
                       zc 
                       RS 
                     
                     = 
                     47 
                   
                   , 
                   
                     u 
                     = 
                     0 
                   
                   , 
                   
                     
                       v 
                       = 
                       0 
                     
                     ; 
                     
                       y 
                       = 
                       
                         47 
                         / 
                         31 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     q 
                     = 
                     
                       
                         
                           ⌊ 
                           
                             
                               47 
                               31 
                             
                             + 
                             0.5 
                           
                           ⌋ 
                         
                         + 
                         
                           
                             ⌊ 
                             
                               
                                 0 
                                 + 
                                 1 
                               
                               2 
                             
                             ⌋ 
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     ⌊ 
                                     
                                       
                                         47 
                                         31 
                                       
                                       + 
                                       0.5 
                                     
                                     ⌋ 
                                   
                                   - 
                                   
                                     47 
                                     31 
                                   
                                 
                                 ⌋ 
                               
                               + 
                               0 
                             
                           
                         
                       
                       = 
                       2 
                     
                   
                 
               
               
                 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0133]    So, for 4 RB length, the first base sequence number (v=0) in the first group (u=0) is 2 (q=2). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       
                         reference 
                         , 
                         zc 
                       
                     
                     = 
                     31 
                   
                   , 
                   
                     
                       N 
                       zc 
                       RS 
                     
                     = 
                     71 
                   
                   , 
                   
                     u 
                     = 
                     0 
                   
                   , 
                   
                     
                       v 
                       = 
                       0 
                     
                     ; 
                     
                       y 
                       = 
                       
                         71 
                         / 
                         31 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     q 
                     = 
                     
                       
                         
                           ⌊ 
                           
                             
                               71 
                               31 
                             
                             + 
                             0.5 
                           
                           ⌋ 
                         
                         + 
                         
                           
                             ⌊ 
                             
                               
                                 0 
                                 + 
                                 1 
                               
                               2 
                             
                             ⌋ 
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     ⌊ 
                                     
                                       
                                         71 
                                         31 
                                       
                                       + 
                                       0.5 
                                     
                                     ⌋ 
                                   
                                   - 
                                   
                                     71 
                                     31 
                                   
                                 
                                 ⌋ 
                               
                               + 
                               0 
                             
                           
                         
                       
                       = 
                       2 
                     
                   
                 
               
               
                 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0134]    So, for 6 RB length, the first base sequence number (v=0) in the first group (u=0) is 2 (q=2). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       
                         reference 
                         , 
                         zc 
                       
                     
                     = 
                     31 
                   
                   , 
                   
                     
                       N 
                       zc 
                       RS 
                     
                     = 
                     211 
                   
                   , 
                   
                     u 
                     = 
                     0 
                   
                   , 
                   
                     
                       v 
                       = 
                       0 
                     
                     ; 
                     
                       y 
                       = 
                       
                         211 
                         / 
                         31 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     q 
                     = 
                     
                       
                         
                           ⌊ 
                           
                             
                               211 
                               31 
                             
                             + 
                             0.5 
                           
                           ⌋ 
                         
                         + 
                         
                           
                             ⌊ 
                             
                               
                                 0 
                                 + 
                                 1 
                               
                               2 
                             
                             ⌋ 
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     ⌊ 
                                     
                                       
                                         211 
                                         31 
                                       
                                       + 
                                       0.5 
                                     
                                     ⌋ 
                                   
                                   - 
                                   
                                     211 
                                     31 
                                   
                                 
                                 ⌋ 
                               
                               + 
                               0 
                             
                           
                         
                       
                       = 
                       7 
                     
                   
                 
               
               
                 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0135]    So, for 18 RB length, the first base sequence number (v=0) in the first group (u=0) is 7 (q=7). 
         [0136]    For the above cases, the selected root indexes (q) correspond to the data in tables 6˜8 which are generated based on 3 RB length. 
         [0137]    In another example, if the N reference,zc =47 (based on 4 RB length), the method for selecting the second group (“u”=1) when 1) Nzc=59, 2) Nzc=107 3) Nzc=139 is as follows. In the following examples, the equation 18 is used. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       
                         reference 
                         , 
                         zc 
                       
                     
                     = 
                     47 
                   
                   , 
                   
                     
                       N 
                       zc 
                       RS 
                     
                     = 
                     59 
                   
                   , 
                   
                     u 
                     = 
                     1 
                   
                   , 
                   
                     
                       v 
                       = 
                       0 
                     
                     ; 
                     
                       y 
                       = 
                       
                         
                           59 
                           / 
                           47 
                         
                         * 
                         2 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     q 
                     = 
                     
                       
                         
                           ⌊ 
                           
                             
                               
                                 59 
                                 · 
                                 2 
                               
                               47 
                             
                             + 
                             0.5 
                           
                           ⌋ 
                         
                         + 
                         
                           
                             ⌊ 
                             
                               
                                 0 
                                 + 
                                 1 
                               
                               2 
                             
                             ⌋ 
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     ⌊ 
                                     
                                       
                                         
                                           59 
                                           · 
                                           2 
                                         
                                         47 
                                       
                                       + 
                                       0.5 
                                     
                                     ⌋ 
                                   
                                   - 
                                   
                                     
                                       59 
                                       · 
                                       2 
                                     
                                     47 
                                   
                                 
                                 ⌋ 
                               
                               + 
                               0 
                             
                           
                         
                       
                       = 
                       3 
                     
                   
                 
               
               
                 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0138]    So, for 5 RB length, the first base sequence number (v=0) in the second group (u=1) is 3 (q=3). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       
                         reference 
                         , 
                         zc 
                       
                     
                     = 
                     47 
                   
                   , 
                   
                     
                       N 
                       zc 
                       RS 
                     
                     = 
                     107 
                   
                   , 
                   
                     u 
                     = 
                     1 
                   
                   , 
                   
                     
                       v 
                       = 
                       0 
                     
                     ; 
                     
                       y 
                       = 
                       
                         
                           107 
                           / 
                           47 
                         
                         * 
                         2 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     q 
                     = 
                     
                       
                         
                           ⌊ 
                           
                             
                               
                                 107 
                                 · 
                                 2 
                               
                               47 
                             
                             + 
                             0.5 
                           
                           ⌋ 
                         
                         + 
                         
                           
                             ⌊ 
                             
                               
                                 0 
                                 + 
                                 1 
                               
                               2 
                             
                             ⌋ 
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     ⌊ 
                                     
                                       
                                         
                                           107 
                                           · 
                                           2 
                                         
                                         47 
                                       
                                       + 
                                       0.5 
                                     
                                     ⌋ 
                                   
                                   - 
                                   
                                     
                                       107 
                                       · 
                                       2 
                                     
                                     47 
                                   
                                 
                                 ⌋ 
                               
                               + 
                               0 
                             
                           
                         
                       
                       = 
                       5 
                     
                   
                 
               
               
                 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0139]    So, for 9 RB length, the first base sequence number (v=0) in the second group (u=1) is 5 (q=5). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       
                         reference 
                         , 
                         zc 
                       
                     
                     = 
                     47 
                   
                   , 
                   
                     
                       N 
                       zc 
                       RS 
                     
                     = 
                     139 
                   
                   , 
                   
                     u 
                     = 
                     1 
                   
                   , 
                   
                     
                       v 
                       = 
                       0 
                     
                     ; 
                     
                       y 
                       = 
                       
                         
                           139 
                           / 
                           47 
                         
                         * 
                         2 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     q 
                     = 
                     
                       
                         
                           ⌊ 
                           
                             
                               
                                 139 
                                 · 
                                 2 
                               
                               47 
                             
                             + 
                             0.5 
                           
                           ⌋ 
                         
                         + 
                         
                           
                             ⌊ 
                             
                               
                                 0 
                                 + 
                                 1 
                               
                               2 
                             
                             ⌋ 
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 ⌊ 
                                 
                                   
                                     ⌊ 
                                     
                                       
                                         
                                           139 
                                           · 
                                           2 
                                         
                                         47 
                                       
                                       + 
                                       0.5 
                                     
                                     ⌋ 
                                   
                                   - 
                                   
                                     
                                       139 
                                       · 
                                       2 
                                     
                                     47 
                                   
                                 
                                 ⌋ 
                               
                               + 
                               0 
                             
                           
                         
                       
                       = 
                       6 
                     
                   
                 
               
               
                 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0140]    So, for 12 RB length, the first base sequence number (v=0) in the second group (u=1) is 6 (q=6). 
         [0141]    In another embodiment of the present invention, the equations 17 and 18 can be replaced as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       q 
                       = 
                       
                         
                           round 
                            
                           
                             ( 
                             y 
                             ) 
                           
                         
                         + 
                         
                           
                             floor 
                              
                             
                               ( 
                               
                                 
                                   v 
                                   + 
                                   1 
                                 
                                 2 
                               
                               ) 
                             
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 floor 
                                  
                                 
                                   ( 
                                   
                                     
                                       round 
                                        
                                       
                                         ( 
                                         y 
                                         ) 
                                       
                                     
                                     - 
                                     y 
                                   
                                   ) 
                                 
                               
                               + 
                               v 
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           y 
                         
                         = 
                         
                           
                             
                               ( 
                               
                                 
                                   N 
                                   zc 
                                   RS 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                             · 
                             
                               ( 
                               
                                 u 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               N 
                               
                                 reference 
                                 , 
                                 zc 
                               
                               RS 
                             
                             - 
                             1 
                           
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         u 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             29 
                           
                           } 
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         v 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               
                                 floor 
                                  
                                 
                                   ( 
                                   
                                     
                                       N 
                                       ZC 
                                       RS 
                                     
                                     / 
                                     30 
                                   
                                   ) 
                                 
                               
                               - 
                               1 
                             
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     20 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
                                 1 
                               
                               2 
                             
                             ) 
                           
                         
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     floor 
                                      
                                     
                                       ( 
                                       
                                         y 
                                         + 
                                         0.5 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
                             + 
                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               - 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             N 
                             
                               reference 
                               , 
                               zc 
                             
                             RS 
                           
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     21 
                   
                   ] 
                 
               
             
           
         
       
     
         [0142]    Because “round (y)” and “floor (y+0.5)” are actually equivalent, the equations 20 and 21 have the same meaning. 
         [0143]    In another embodiment of the present invention, the equations 17 and 18 can be replaced as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         q 
                         = 
                         
                           
                             round 
                              
                             
                               ( 
                               y 
                               ) 
                             
                           
                           + 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     v 
                                     + 
                                     1 
                                   
                                   2 
                                 
                                 ) 
                               
                             
                             · 
                             
                               
                                 ( 
                                 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               
                                 
                                   floor 
                                    
                                   
                                     ( 
                                     
                                       
                                         round 
                                          
                                         
                                           ( 
                                           y 
                                           ) 
                                         
                                       
                                       - 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 v 
                               
                             
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         
                           where 
                            
                           
                               
                           
                            
                           y 
                         
                         = 
                         
                           
                             round 
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               
                                 N 
                                 
                                   reference 
                                   , 
                                   zc 
                                 
                                 RS 
                               
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     22 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
                                 1 
                               
                               2 
                             
                             ) 
                           
                         
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     floor 
                                      
                                     
                                       ( 
                                       
                                         y 
                                         + 
                                         0.5 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
                             + 
                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           floor 
                           ( 
                           
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               
                                 N 
                                 
                                   reference 
                                   , 
                                   zc 
                                 
                                 RS 
                               
                             
                             + 
                             0.5 
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     23 
                   
                   ] 
                 
               
             
           
         
       
     
         [0144]    These equations correspond to various grouping method explained with regard to the above mentioned tables. 
         [0145]    If the maximum number of sequences, which can be grouped in one group, are predetermined to 2, the equations 17-18, 20-21 and 22-23 can be simplified as follows, respectively. 
         [0000]    
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           N 
                           
                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     24 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           N 
                           
                             reference 
                             , 
                             zc 
                           
                           RS 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     25 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               - 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             N 
                             
                               reference 
                               , 
                               zc 
                             
                             RS 
                           
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     26 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 zc 
                                 RS 
                               
                               - 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               u 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             N 
                             
                               reference 
                               , 
                               zc 
                             
                             RS 
                           
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     27 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         round 
                          
                         
                           ( 
                           y 
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           round 
                           ( 
                           
                             
                               N 
                               zc 
                               RS 
                             
                             
                               N 
                               
                                 reference 
                                 , 
                                 zc 
                               
                               RS 
                             
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     28 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         v 
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             floor 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 
                                   N 
                                   zc 
                                   RS 
                                 
                                 
                                   N 
                                   
                                     reference 
                                     , 
                                     zc 
                                   
                                   RS 
                                 
                               
                               + 
                               0.5 
                             
                             ) 
                           
                         
                         · 
                         
                           ( 
                           
                             u 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     29 
                   
                   ] 
                 
               
             
           
         
       
     
         [0146]    The equations 17-18, 20-21 and 22-23 are for selecting ZC root index to meet the condition that the term (s 1 /N 1 −s 2 /N 2 ) become close to zero. And, the equations 24-29 are for selecting root index ZC root index when the maximum number of sequences per groups of each length is limited to 2. 
         [0147]    But if we make these equations to be more generalized such that the term (s 1 /N 1 −s 2 /N 2 ) become close to a specific value (T), the following equations can be acquired. In this case, the value “T” can be 0, ½, −½, ⅓, −⅓. But value “T” can have other value. 
         [0148]    In the following equations, the equations 30 and 31 are for selecting ZC root index when the maximum number of sequence per group of each length can have the maximum value. And, the equations 32 and 33 are for selecting ZC root index when the maximum number of sequence per group of each length is limited to 2. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       q 
                       = 
                       
                         
                           round 
                            
                           
                             ( 
                             y 
                             ) 
                           
                         
                         + 
                         
                           
                             floor 
                              
                             
                               ( 
                               
                                 
                                   v 
                                   + 
                                   1 
                                 
                                 2 
                               
                               ) 
                             
                           
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               
                                 floor 
                                  
                                 
                                   ( 
                                   
                                     
                                       round 
                                        
                                       
                                         ( 
                                         y 
                                         ) 
                                       
                                     
                                     - 
                                     y 
                                   
                                   ) 
                                 
                               
                               + 
                               v 
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           y 
                         
                         = 
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               T 
                               + 
                               
                                 
                                   ( 
                                   
                                     u 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 
                                   N 
                                   
                                     reference 
                                     , 
                                     zc 
                                   
                                   RS 
                                 
                               
                             
                             ) 
                           
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         u 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             29 
                           
                           } 
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         v 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               
                                 floor 
                                  
                                 
                                   ( 
                                   
                                     
                                       N 
                                       ZC 
                                       RS 
                                     
                                     / 
                                     30 
                                   
                                   ) 
                                 
                               
                               - 
                               1 
                             
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     30 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         floor 
                          
                         
                           ( 
                           
                             y 
                             + 
                             0.5 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               
                                 v 
                                 + 
                                 1 
                               
                               2 
                             
                             ) 
                           
                         
                         · 
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     floor 
                                      
                                     
                                       ( 
                                       
                                         y 
                                         + 
                                         0.5 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   y 
                                 
                                 ) 
                               
                             
                             + 
                             v 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         where 
                          
                         
                             
                         
                          
                         y 
                       
                       = 
                       
                         
                           N 
                           zc 
                           RS 
                         
                         · 
                         
                           ( 
                           
                             T 
                             + 
                             
                               
                                 ( 
                                 
                                   u 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               
                                 N 
                                 
                                   reference 
                                   , 
                                   zc 
                                 
                                 RS 
                               
                             
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       u 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           29 
                         
                         } 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       v 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           … 
                            
                           
                               
                           
                           , 
                           
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     ZC 
                                     RS 
                                   
                                   / 
                                   30 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     31 
                   
                   ] 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     
                       q 
                       = 
                       
                         
                           round 
                            
                           
                             ( 
                             y 
                             ) 
                           
                         
                         + 
                         
                           v 
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   2 
                                    
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           y 
                         
                         = 
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               T 
                               + 
                               
                                 
                                   ( 
                                   
                                     u 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 
                                   N 
                                   
                                     reference 
                                     , 
                                     zc 
                                   
                                   RS 
                                 
                               
                             
                             ) 
                           
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         u 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             29 
                           
                           } 
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         v 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     32 
                   
                   ] 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     
                       q 
                       = 
                       
                         
                           floor 
                            
                           
                             ( 
                             
                               y 
                               + 
                               0.5 
                             
                             ) 
                           
                         
                         + 
                         
                           v 
                           · 
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             
                               floor 
                                
                               
                                 ( 
                                 
                                   2 
                                    
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           y 
                         
                         = 
                         
                           
                             N 
                             zc 
                             RS 
                           
                           · 
                           
                             ( 
                             
                               T 
                               + 
                               
                                 
                                   ( 
                                   
                                     u 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 
                                   N 
                                   
                                     reference 
                                     , 
                                     zc 
                                   
                                   RS 
                                 
                               
                             
                             ) 
                           
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         u 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             29 
                           
                           } 
                         
                       
                       , 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         v 
                         ∈ 
                         
                           { 
                           
                             0 
                             , 
                             1 
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     33 
                   
                   ] 
                 
               
             
           
         
       
     
         [0149]    It will be apparent to those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit and essential characteristics of the invention. Thus, the above embodiments are to be considered in all respects as illustrative and not restrictive. The scope of the invention should be determined by reasonable interpretation of the appended claims and all change which comes within the equivalent scope of the invention are included in the scope of the invention. 
         [0150]    According to the embodiments of the present invention, inter cell interference caused by using variable length sequences can be minimized. And, if each grouped base sequence is allocated to specific cell or Node B, UE(s) can use variable length sequence as reference signal. 
         [0151]    These methods are appropriate to be employed in 3GPP LTE (3 rd  Generation Partnership Project Long Term Evolution) system. But, those skilled in the art can easily understand that these methods can be employed to any wireless communication system using various length sequences as a reference signal sequences. 
         [0152]    Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims.