partial period crosscorrelations of geometric sequences for a binary pseudorandom sequence s sub i with period n the partial period autocorrelation function a sub s spl tau k d is defined by correlating the portion of the sequence within a window of size d and start position k with the portion in another window of the same size but starting spl tau steps later in the sequence a distribution of possible partial period autocorrelation values is obtained by allowing the start position k to vary over all possible values o spl les k

meromorphic solutions of generalized inviscid burgers equations and a family of quadratic pdes abstract meromorphic solutions of generalized inviscid burgers equations in c 2 are characterized the results are employed to characterize meromorphic solutions of the partial differential equation p u x u y 0 where p is the general irreducible quadratic polynomial in c 2

almost perfect polyphase sequences with small phase alphabet new classes of polyphase sequences with small phase alphabets of size k are presented these almost perfect sequences of length n have a vanishing periodic autocorrelation function spl theta spl tau for all spl tau spl ne 0 mod n k the sequences are derived from q ary m sequences by a k valued character operation

enumeration and criteria for cyclically shift distinct gmw sequences gordon mills welch gmw sequences also called cascaded gmw sequences have two level autocorrelations this property makes them widely used in various communication and cryptographic systems the generation of q ary gmw sequences of period q sup n 1 involves three types of parameters to determine whether gmw sequences are cyclically shift distinct for differing parameters has remained an open question until now in this paper we completely solve this problem for varying all three types of parameters we find a criterion for cyclically shift distinct q ary gmw sequences of period q sup n 1 and obtain the number of such sequences for the special case of q 2 this solution facilitates counting the number of cyclic hadamard difference sets which correspond to binary gmw sequences of period 2 sup n 1

theory and applications of q ary interleaved sequences a new class of q ary sequences called interleaved sequence is introduced their periods shift equivalence linear spans and autocorrelation functions are derived the interleaved sequences include a large number of popular sequences such as multiplexed sequences clock controlled sequences kasami 1966 sequences gmw sequences geometric sequences and no 1989 sequences a special class of the interleaved sequences is constructed by mapping gf q sup m sequences into gf q sequences in terms of different bases of gf q sup m over gf q as an application of the theory of interleaved sequences some new families of binary pseudo random sequences are constructed which have large linear spans optimal periodic cross autocorrelation functions balance and the rapidly hopped properties a complete comparison of the new family of sequences with the gold sequence family the kasami small and large set sequence families the bent function sequence family and the no sequence family is discussed this shows that the new sequence families have important advantages for use in spread spectrum multiple access communication systems

a class of pseudonoise sequences over gf p with low correlation zone a new class of pseudonoise sequences over gf p based on gordon mills welch 1962 sequences is constructed the sequences have the property that in a specified zone the out of phase autocorrelation and cross correlation values are all equal to 1 such sequences with low correlation zone lcz are suitable for approximately synchronized code division multiple access cdma system

some malmquist type theorems of partial differential equations on cn abstract in this paper using the techniques and some basic results from the value distribution theory in several complex variables we investigate the existence problem of meromorphic solutions of a class of partial differential equations on c n some malmquist type theorems of partial differential equations on c n are established a rellich type theorem of partial differential equations on c n is also obtained several examples are given to complement the theory

new classes of optimal frequency hopping sequences by interleaving techniques in this paper we construct new classes of optimal frequency hopping sequences fhss with respect to the lempel greenberger bound and the peng fan bound by interleaving techniques which are used to construct a sequence of length kn from k sequences of length n we first give two generic constructions for optimal fhs sets from some known optimal fhs sets by interleaving techniques and present some examples of new optimal fhs sets we then design new optimal fhss whose parameters include those of the known optimal constructions with length kn and frequency set size n for some positive integers k and n we also construct optimal fhs sets of length kp from power residue sequences for any odd prime p and 2 les k p in particular our constructions give several new parameters not covered in the literature which are summarized in i and ii

the linear complexity of binary sequences with optimal autocorrelation binary sequences with optimal autocorrelation are needed in many applications two constructions of binary sequences with optimal autocorrelation of period n 0 mod 4 are investigated the two constructions are powerful and generic in the sense that many classes of binary sequences with optimal autocorrelation could be obtained from binary sequences with ideal autocorrelation general results on the minimal polynomials of these binary sequences are derived based on the results both the linear complexities and the minimal polynomials are determined

optimal sets of frequency hopping sequences with large linear spans frequency hopping fh is one of the basic spread coding technologies in spread spectrum communications fh sequences are needed in fh code division multiple access cdma systems for the anti jamming purpose fh sequences are required to have a large linear span a few optimal sets of fh sequences are available in the literature however their sequences have very small linear spans it is known that an optimal set of fh sequences could be transformed to another optimal set of fh sequences with large linear spans by a power permutation if the power is chosen properly see c ding and j yin ieee trans inf theory vol it 54 pp 3741 3745 2008 the objective of this paper is to investigate this idea of c ding and j yin further and determine the linear span of the fh sequences in the optimal sets obtained by applying a power permutation to some existing optimal sets of fh sequences

p ary unified sequences p ary extended d form sequences with the ideal autocorrelation property in this paper for a prime number p a construction method to generate p ary d form sequences with the ideal autocorrelation property is proposed and using the ternary sequences found by helleseth kumar and martinsen 2000 ternary d form sequences with the ideal autocorrelation property are constructed by combining the methods for generating p ary extended sequences a special case of geometric sequences and p ary d form sequences a construction method of p ary unified extended d form sequences which also have the ideal autocorrelation property is proposed this is a very general class of p ary sequences including the binary and nonbinary extended sequences and the d form sequences from the ternary sequences by helleseth kumar and martinsen ternary unified sequences with the ideal autocorrelation property are also generated

new design of low correlation zone sequence sets in this paper we present several construction methods for low correlation zone lcz sequence sets first we propose a design scheme for binary lcz sequence sets with parameters 2n 1 2 m l 2 in this scheme we can freely set the lcz length l and the resulting lcz sequence sets have the size m which is almost optimal with respect to tang fan and matsufuji bound second given a q ary lcz sequence set with parameters n m l epsi and even q we construct another q ary lcz sequence set with parameters 2n 2m l 2epsi or 2n 2m l 1 2epsi especially the new set with parameters 2n 2m l 2 can be optimal in terms of the set size if a q ary optimal lcz sequence set with parameters n m l 1 is used

on the existence of cyclic hadamard difference sets the main conjecture of this article is the following if a cyclic v 4n 1 k 2n 1 spl lambda n 1 hadamard difference set exists the the value of v must be either a prime or a product of twin primes or one less than a power of 2 six cases v 399 495 627 651 783 and 975 which were once listed as the possible exceptions for v

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

on entire solutions to eikonal type equations abstract this paper discusses equivalence conditions on entire solutions to eikonal type nonlinear partial differential equations u z 1 2 u z 2 2 p z 1 z 2 e g z 1 z 2 in c 2 for polynomials g z 1 z 2 p z 1 z 2 all our results are supplemented by examples for accuracy

q ary cascaded gmw sequences cascaded gmw sequences over gf q of arbitrary characteristic are investigated their periods are derived as compared with the existing results on such sequences substantially extended and improved theorems concerning their linear spans and autocorrelation functions are obtained a criterion and an algorithm for constructing cascaded gmw sequences that have much larger linear spans than gmw sequences with the same periods are given these provide a new class of complex valued sequences which have larger linear spans and two valued autocorrelation functions

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings we construct new sequences over finite rings having optimal hamming correlation properties these sequences are useful in frequency hopping multiple access fhma spread spectrum communication systems our constructions can be classified into linear and nonlinear categories both giving optimal hamming correlations according to lempel greenberger 1974 bound the nonlinear sequences have large linear complexity and can be seen as a generalized version of gmw sequences over fields

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

large families of sequences with near optimal correlations and large linear span in order to build spread spectrum communication systems based on the cdma paradigm it is necessary to have large families of binary sequences with low pairwise correlation values for these systems to have resistance to certain cryptanalytic attacks and resistance to jamming the sequences must have large linear span we describe certain families of sequences that have these desirable properties the sequences are based on families of quadratic forms over finite fields

on the linear complexity of some new q ary sequences some new q ary sequences with period q 3 e k 1 q p m p an odd prime m e k integers are first constructed and then inspired by antweiler s method their linear complexity is examined the exact value of linear complexity k 6e w is determined when email protected i 1 wp e i furthermore an upper bound of the linear complexity is given for the other values of r our results show that this sequence has larger linear span than gmw sequence with the same parameters finally the results of a maple program are included to illustrate the validity of the results

orthogonal periodic sequences derived from m sequences on gf q a novel construction is proposed to generate orthogonal periodic sequences whose elements consist of at most q complex numbers which are not expressed in the power of complex primitive roots of unity the orthogonal periodic sequences are generated by mapping m sequences on gf q into complex periodic sequences

on meromorphic solutions of first order briot bouquet type pdes abstract utilizing a theorem of coman and poletsky see 4 which characterizes the factorization of algebraically dependent meromorphic functions and the parametrization of the polynomial functional equation they satisfy along with results from nevanlinna theory we obtain results on the meromorphic solutions of the first order briot bouquet type pdes p u u x 0

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

new construction for binary sequences of period p sup m 1 with optimal autocorrelation using z 1 sup d az sup d b we present a construction for binary sequences s t of period n p sup m 1 for an odd prime p based on the polynomial z 1 sup d az sup d b and discuss them in some cases of parameters p m d a and b we show that new sequences from our construction are balanced or almost balanced and have optimal three level autocorrelation for the case when the polynomial z 1 sup d z sup d a can be transformed into the form z sup 2 c we also derive the distribution of autocorrelation values they take on the sequences satisfy constant on the coset property and we show that there are more than one characteristic phases with constant on the coset property some other interesting properties of those sequences are presented for the cases when the polynomial z 1 sup d z sup d a cannot be transformed into the form z sup 2 c we performed extensive computer search and results are summarized based on these results some open problems are formulated

on the linear complexity of legendre sequences we determine the linear complexity of all legendre sequences and the monic feedback polynomial of the shortest linear feedback shift register that generates such a legendre sequence the result shows that legendre sequences are quite good from the linear complexity viewpoint

on the linear complexity of hall s sextic residue sequences in this correspondence the characteristic polynomial and hence the linear complexity of hall s sextic residue sequences are determined

on meromorphic solutions of some algebraic partial differential equations oncn abstract applying the techniques from nevanlinna theory of value distribution theory of meromorphic functions oncn we investigate the existence problem of some meromorphic solutions and obtain a satisfactory malmquist type theorem for a class of algebraic partial differential equations oncnwhich improves some earlier main results we give several examples to complement our results

binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation generated by the polynomial z sup d z 1 sup d we present a construction for binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation property using the polynomial z sup d z 1 sup d we show that the sequence obtained from the polynomial becomes an m sequence for certain values of d we also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k spl plusmn 1 where k is a positive integer these new sequences are represented using a trace function and the results are tabulated

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

bounds on partial correlations of sequences two approaches to bounding the partial auto and crosscorrelations of binary sequences are considered the first approach uses the discrete fourier transform and bounds for character sums to obtain bounds on partial autocorrelations of m sequences and on the partial auto and crosscorrelations for the small kasami sets and dual bch families of sequences the second approach applies to binary sequences obtained by interleaving m sequences a bound on the peak partial correlation of such sequences is derived in terms of the peak partial autocorrelation of the underlying m sequences the bound is applied to gmw no 1987 and other families of sequences for particular parameters a comparison of the two approaches shows that the elementary method gives generally weaker results but is more widely applicable on the other hand both methods show that well known sequence families can have favorable partial correlation characteristics making them useful in certain spread spectrum applications

d form sequences families of sequences with low correlation values and large linear spans large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems the author describes a method for constructing such families from families of homogeneous functions over finite fields satisfying certain properties he then uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than no sequences no 1988

autocorrelation values of generalized cyclotomic sequences of order two the generalized cyclotomic sequence of order two has several good randomness properties and behaves like the legendre sequence in several aspects we calculate the autocorrelation values of the generalized cyclotomic sequence of order two our result shows that this sequence could have very good autocorrelation property and pattern distributions of length two if the two primes are chosen properly

new constructions of quaternary low correlation zone sequences in this paper given a composite integer n we propose a method of constructing quaternary low correlation zone lcz sequences of period 2 sup n 1 from binary sequences of the same length with ideal autocorrelation these new sequences are optimal with respect to the bound by tang fan and matsufuji the correlation distributions of these new quaternary lcz sequences constructed from m sequences and gordon mills welch gmw sequences are derived

linear span of extended sequences and cascaded gmw sequences in this correspondence the linear span of extended sequences of period 2 sup em 1 which are constructed from the ideally correlated sequences of period of 2 sup m 1 is derived it is also shown that the linear span of cascaded gordon mills welch gmw sequences can be derived in the same context as examples the linear span of extended legendre sequences and cascaded gmw sequences with triple trace are computed

positive solutions to some systems of coupled nonlinear schrodinger equations abstract we study the existence of nontrivial bound state solutions to the following system of coupled nonlinear time independent schrodinger equations u j j u j j u j 3 k 1 k j n j k u j u k 2 u j w 1 2 r n j 1 n where n 1 2 3 j j 0 for j 1 n the coupling parameters j k k j r for j k 1 n j k precisely we prove the existence of nonnegative bound state solutions for suitable conditions on the coupling factors additionally with more restrictive conditions on the coupled parameters we show that the bound states founded are positive

generalization of gmw sequences and no sequences gmw sequences and families of no sequences are generalized generalized gmw sequences have ideal autocorrelation and balance properties and generalized no sequences also have optimal correlation properties in terms of welch s lower bound the linear spans of the generalized gmw and no sequences appear to be large although there is not at present a closed form expression for the linear span a count of the numbers of cyclically distinct generalized gmw sequences and generalized no sequences that can be constructed is provided generalized gmw sequences have also been found in the literature by klapper et al 1993 under the name cascaded gmw sequences

global bifurcation results for a semilinear elliptic equation on all of mathbb r n we prove the existence of positive solutions for the semilinear elliptic equation u x g x f u x 0 u 1 for x r lim x u x 0 which arises in population genetics under the hypotheses that n 3 4 5 and g lies in l n 2 ir n we establish the existence of a principal eigenvalue 1 for the corresponding linearized problem and making use of the asymptotic properties of solutions and local and global bifurcation theory prove the existence of a continuum of solutions lying in the space d 1 2 extending from 1 to

entire solutions of certain partial differential equations and factorization of partial derivatives we show that the problem of characterizing entire solutions of certain partial differential equations and the problem of characterizing common right factors of partial derivatives of meromorphic functions in c 2 are closely related and characterizations will be given using their relations

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

a new class of nonlinear pn sequences over gf q sup n a new class of pseudo random sequences called cascaded gmw type permutation polynomial cgpp sequences over gp q sup n is constructed using a system of n orthogonal cascaded gmw functions in gf q their statistical properties are given classification evaluation and implementation of the cgpp sequences are derived a sequence generated by mapping elements of a cgpp sequence into gf q is also presented

variational perturbative methods and bifurcation of bound states from the essential spectrum this paper consists of two main parts the first deals with a perturbative method in critical point theory and can be seen as the generalisation and completion of some earlier results the second part is concerned with applications of the abstract setup to the existence of bound states of a class of elliptic differential equations that branch off from the infimum of the essential spectrum

relationships between m sequences over gf q and gf q sup m it is shown that m sequences over gf q sup m of length q sup nm 1 corresponding to primitive polynomials in gf q sup m x of degree n can be generated from known m sequences over gf q of length q sup nm 1 obtained from primitive polynomials in gf q x of degree mn a procedure for generating the m sequences over gf q sup 2 from m sequences over gf q was given which enables the generation of m sequences over gf p sup 2n in addition it was shown that all of the primitive polynomials in gf q sup m x can be obtained from a complete set of the primitive polynomials in gf q x

a solution method for autonomous first order algebraic partial differential equations in this paper we present a procedure for solving first order autonomous algebraic partial differential equations in an arbitrary number of variables the method uses rational parametrizations of algebraic hyper surfaces and generalizes a similar procedure for first order autonomous ordinary differential equations in particular we are interested in rational solutions and present certain classes of equations having rational solutions however the method can also be used for finding non rational solutions

periodic binary sequences with the trinomial property periodic binary sequences with the trinomial property are considered some necessary and sufficient conditions for trinomial pairs of a nonlinear sequence of period 2 sup n 1 as well as classifications for trinomial pairs are derived complete searches for trinomial pairs of sequences have been completed for 3 spl les n spl les 17 we list them here for n spl les 12

optimal frequency hopping sequences a combinatorial approach frequency hopping multiple access fhma spread spectrum communication systems employing multiple frequency shift keying mfsk as data modulation technique are investigated from a combinatorial approach a correspondence between optimal frequency hopping fh sequences and partition type difference packings is first established by virtue of this correspondence fhma systems with a single optimal fh sequence each are constructed from various combinatorial structures such as affine geometries cyclic designs and difference families combinatorial recursive constructions are also presented many new infinite series of optimal fh sequences are thus obtained these new fh sequences are also useful in ultra wideband uwb communication systems

decompositions of difference sets abstract we characterize those symmetric designs with a singer group g which admit a quasi regular g invariant partition into strongly induced symmetric subdesigns in terms of the corresponding difference sets the set associated with the larger design can be decomposed into a difference set describing the small designs and a suitable relative difference set this generalizes the decomposition of the classical design with the complements of hyperplanes in pg m 1 q as blocks into sub designs arising from pg d 1 q whenever d divides m parametrically these geometrical examples provide the only known examples of the situation we are studying but there are many nonisomorphic examples with the same parameters namely the complements of the classical gmw designs and some generalizations we also discuss the possibilities for obtaining new difference sets in this way and point out a connection to the recent constructions of ionin for symmetric designs

cross correlation of p ary gmw sequences the cross correlation function of p ary p prime gmw sequences is investigated the well known m sequences are incorporated in these sequences gmw sequences also have the two level autocorrelation function but their linear span may be much larger than those of m sequences the calculation of the cross correlation function of gmw sequences is reduced to the cross correlation of the m sequences because many results on this kind of sequence are known in the literature only the cross correlation function of an m sequence with a gmw sequence has been known up to now

new self dual codes over gf 4 with the highest known minimum weights the purpose of this correspondence is to construct new hermitian self dual codes over gf 4 of lengths 22 24 26 32 and 34 which have the highest known minimum weights in particular for length 22 we construct eight new extremal self dual 22 11 8 codes over gf 4 which do not have a nontrivial automorphism of odd order the existence of such codes has been left open since 1991 by huffman

binary sequences with optimal autocorrelation sequences have important applications in ranging systems spread spectrum communication systems multi terminal system identification code division multiple access communication systems global positioning systems software testing circuit testing computer simulation and stream ciphers sequences and error correcting codes are also closely related in this paper we give a well rounded treatment of binary sequences with optimal autocorrelation we survey known ones and construct new ones

frequency hopping sequences with optimal partial autocorrelation properties we classify some p sup k ary p prime k integer generalized m sequences and generalized gordon mills welch gmw sequences of period p sup 2k 1 over a residue class ring r gf p spl xi spl xi sup k having optimal partial hamming autocorrelation properties in frequency hopping fh spread spectrum systems these sequences are useful for synchronizing process suppose for example that a transmitting p sup k ary fh patterns of period p sup 2k 1 are correlated at a receiver usually the length of a correlation window denoted by l is shorter than the pattern s overall period in that case the maximum value of the out of phase hamming autocorrelation is lower bounded by spl lceil l p sup k 1 spl rceil but the classified sequences achieve this bound with equality for any positive integer l

trace representation and linear complexity of binary e th power residue sequences of period p let p ef 1 be an odd prime for some e and e and let f be the finite field with fp elements in this paper we explicitly describe the trace representations of the binary characteristic sequences of period p of all the cyclic difference sets d which are some union of cosets of eth powers he in fp fp 0 for e 12 for this we define eth power residue sequences of period p which include all the binary characteristic sequences mentioned above as special cases and reduce the problem of determining their trace representations to that of determining the values of the generating polynomials of cosets of he in f at some primitive pth root of unity and some properties of these values are investigated based on these properties the trace representation and linear complexity not only of the characteristic sequences of all the known eth residue difference sets but of all the sixth power residue sequences are determined furthermore we have determined the linear complexity of a nonconstant eth power residue sequence for any e to be either p 1 or p whenever e p 1 n 1 where n is the order of 2 mod p

complex sequences over gf p sup m with a two level autocorrelation function and a large linear span new complex sequences with elements are proposed that have constant absolute values of 1 the periodic autocorrelation functions of these sequences are shown to be two level the sequences are generated by three consecutive mapping processes the number of sequences of fixed length is determined which is larger than the number of binary sequences for cryptographical reasons the large linear span of the sequences is of great interest the linear span of the new sequences is examined and is proven to be larger than the linear span of complex m sequences if the parameters of the mapping processes are appropriately chosen the formula for generating the sequences is generalized to enlarge the linear span of sequences

new constructions for optimal sets of frequency hopping sequences in this paper two generic constructions of optimal frequency hopping sequence fhs sets employing d form functions with difference balanced property are presented they generalize the previous constructions of optimal fhs sets using m sequences and produce new optimal fhs sets that cannot be produced by the earlier constructions by choosing appropriate d form functions with difference balanced property both constructions lead to fhss with large linear complexity in addition one of the proposed constructions gives new optimal parameters of fhs sets

the linear complexity of some binary sequences with three level autocorrelation binary sequences with good autocorrelation are needed in many applications a construction of binary sequences with three level autocorrelation was recently presented this construction is generic and powerful in the sense that many classes of binary sequences with three level autocorrelation could be obtained from any difference set with singer parameters the objective of this paper is to determine both the linear complexity and the minimal polynomial of two classes of binary sequences i e the class based on the singer difference set and the class based on the gmw difference set

on the linear complexity of binary sequences of period 4n with optimal autocorrelation value magnitude three classes of binary sequences of period 4n with optimal autocorrelation value magnitude have been constructed by tang and gong based on interleaving certain kinds of sequences of period n i e the legendre sequence twin prime sequence and generalized gmw sequence in this paper by means of sequence polynomials of the underlying sequences the properties of roots of the corresponding sequence polynomials of the interleaved sequences with period 4n and optimal autocorrelation value magnitude are discussed in the splitting field of xn 1 as a consequence both the minimal polynomials and linear complexities of these three classes of sequences are completely determined except for the case of the sequences obtained from the generalized gmw sequences for the latter the minimal polynomial and linear complexity can be specially obtained if the sequence is constructed based on m sequences instead of generalized gmw sequences