complete mutually orthogonal golay complementary sets from reed muller codes recently golay complementary sets were shown to exist in the subsets of second order cosets of a q ary generalization of the first order reed muller rm code we show that mutually orthogonal golay complementary sets can also be directly constructed from second order cosets of a q ary generalization of the first order rm code this identification can be used to construct zero correlation zone zcz sequences directly and it also enables the construction of zcz sequences with special subsets

an asymptotic membrane like theory for long wave motion in a pre stressed elastic plate an asymptotically consistent two dimensional theory is developed to help elucidate dynamic response in finitely deformed layers the layers are composed of incompressible elastic material with the theory appropriate for long wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function leading order and refined higher order equations for the mid surface deflection are derived in the case of zero normal initial static stress and in plane tension the leading order equation reduces to the classical membrane equation with its refined counterpart also being obtained the theory is applied to a one dimensional edge loading problem for a semi infinite plate in doing so the leading and higher order governing equations are used as inner and outer asymptotic expansions the latter valid within the vicinity of the associated quasi front a solution is derived by using the method of matched asymptotic expansions

sequence folding lattice tiling and multidimensional coding folding a sequence b into a multidimensional box is a well known method which is used as a multidimensional coding technique the operation of folding is generalized in a way that the sequence b can be folded into various shapes and not just a box the novel definition of folding is based on a lattice tiling for the given shape s and a direction in the d dimensional integer grid necessary and sufficient conditions that a lattice tiling for s combined with a direction define a folding of a sequence into s are derived the immediate and most impressive applications are some new lower bounds on the number of dots in two dimensional synchronization patterns asymptotically optimal such patterns were known only for rectangular shapes we show asymptotically optimal such patterns for a large family of hexagons this is also generalized for multidimensional synchronization patterns the best known patterns in terms of dots for circles and other polygons are also given the technique and its application for two dimensional synchronization patterns raises some interesting problems in discrete geometry we will also discuss these problems it is also shown how folding can be used to construct multidimensional error correcting codes finally by using the new definition of folding new types of multidimensional pseudo random arrays with various shapes are generated

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

strong no hit zone sequences for improved quasi orthogonal fhma systems sequence design and performance analysis this paper is focused on the optimal design and performance analysis of a novel class of no hit zone frequency hopping sequences nhz fhss in quasi synchronous fh multiple access qs fhma systems although traditional nhz fhss can offer interference free fhma performance when the signal arrival delay tau does not exceed the width of nhz z mathrm nh i e tau leq z mathrm nh the same performance cannot be guaranteed for tau z mathrm nh in which traditional nhz fhzs may have large hamming correlation which denotes the total number of frequency hits of sequences and consequently poor error probability performance since the strict quasi synchronization i e tau leq z mathrm nh may be hard to maintain at all times in practical fhma networks e g infrastructureless ad hoc networks it is also important to minimize the hamming correlation for time shifts outside of the nhz such fhss are called strong nhz fhss snhz fhss in this paper we derive a lower bound on the maximum hamming correlation outside of the nhz and then present a design algorithm for the optimal snhz fhs set meeting our proposed lower bound with equality we analyze the bit error rate ber performance of the fhma system employing the proposed snhz fhs sets using the average hamming correlation function the theoretical analysis and simulation results show that the proposed optimal snhz fhs sets are feasible for practical fhma networks with relaxed timing requirement and enhanced ber performance

optimal odd length binary z complementary pairs a pair of sequences is called a golay complementary pair gcp if their aperiodic auto correlation sums are zero for all out of phase time shifts existing known binary gcps only have even lengths in the form of 21026 where are non negative integers to fill the gap left by the odd lengths we investigate the optimal oddlength binary pairs which display the closest correlation property to that of gcps our criteria of closeness is that each pair has the maximum possible zero correlation zone zcz width and minimum possible out of zone aperiodic auto correlation sums such optimal pairs are called optimal odd length binary z complementary pairs ob zcp in this paper we show that each optimal ob zcp has maximum zcz width of n 1 2 and minimum out of zone aperiodic sum magnitude of 2 where n denotes the sequence length odd systematic constructions of such optimal op zcps are proposed by insertion and deletion of certain binary gcps which settle the 2011 li fan tang tu open problem positively the proposed optimal ob zcps may serve as a replacement for gcps in many engineering applications where odd sequence lengths are preferred in addition they give rise to a new family of base two almost difference families adf which are useful in studying partially balanced incomplete block design bibd index terms aperiodic correlation almost difference set ads almost difference families adf golay complementary pair gcp zero correlation zone zcz z complementary pair zcp

rudin shapiro like sequences with maximum asymptotic merit factor borwein and mossinghoff investigated the rudin shapiro like sequences which are infinite families of binary sequences usually represented as polynomials each family of rudin shapiro like sequences is obtained from a starting sequence which we call the seed by a recursive construction that doubles the length of the sequence at each step and many sequences produced in this manner have exceptionally low aperiodic autocorrelation borwein and mossinghoff showed that the asymptotic autocorrelation merit factor for any such family is at most 3 and found the seeds of length 40 or less that produce the maximum asymptotic merit factor of 3 the definition of rudin shapiro like sequences was generalized by katz lee and trunov to include sequences with arbitrary complex coefficients among which are families of low autocorrelation polyphase sequences katz lee and trunov proved that the maximum asymptotic merit factor is also 3 for this larger class here we show that a family of such rudin shapiro like sequences achieves asymptotic merit factor 3 if and only if the seed is either of length 1 or is the interleaving of a pair of golay complementary sequences for small seed lengths where this is not possible the optimal seeds are interleavings of pairs that are as close as possible to being complementary pairs and the idea of an almost complementary pair makes sense of remarkable patterns in previously unexplained data on optimal seeds for binary rudin shapiro like sequences

two dimensional spatial signature patterns an optical orthogonal signature pattern code oospc is a collection of 0 1 two dimensional 2 d patterns with good correlation properties i e high autocorrelation peaks with low sidelobes and low cross correlation functions such codes find applications for example to parallelly transmit and access images in multicore fiber code division multiple access cdma networks up to now all work on oospcs has been based on an assumption that at most one pulse per column or one pulse per row and column is allowed in each two dimensional pattern however this restriction may not be required in such multiple access networks if timing information can be extracted from other means rather than from the autocorrelation function a new class of oospcs is constructed without the restriction the relationships between two dimensional binary discrete auto and cross correlation arrays and their corresponding sets for oospcs are first developed in addition new bounds on the size of this special class of oospcs are derived afterwards four algebraic techniques for constructing these new codes are investigated among these constructions some of them achieve the upper bounds with equality and are thus optimal finally the codes generated from some constructions satisfy the restriction of at most one pulse per row or column and hence can be used in applications requiring for example frequency hopping patterns

a generalized construction of multiple complete complementary codes and asymptotically optimal aperiodic quasi complementary sequence sets in recent years complete complementary codes cccs and quasi complementary sequence sets qcsss have found many important applications in multi carrier code division multiple access mc cdma systems for their good correlation properties in this paper we propose a generic construction of multiple sets of cccs over mathbb z n consisting of sequences of length n where n geq 3 is an arbitrary odd integer interestingly the maximum inter set aperiodic cross correlation magnitude of the proposed cccs is upper bounded by n it turns out that the combination of the generated cccs results in a new set of sequences to obtain asymptotically optimal and near optimal aperiodic qcsss the proposed construction includes a recent optimal construction of qcsss with prime length as a special case and leads to asymptotically optimal qcsss with new flexible parameters

new complete complementary codes for peak to mean power control in multi carrier cdma owing to the zero non trivial aperiodic correlation sum properties complete complementary codes ccc have been applied to asynchronous multi carrier code division multiple access mc cdma communications in order to provide zero interference performance when each complementary code is arranged to be a matrix the peak to mean envelope power ratio pmepr of the ccc mc cdma system is determined by the column sequences of the complementary matrices the existing ccc have the column sequence pmepr of m where m denotes the number of subcarriers in a ccc mc cdma system in practice m is generally large and a pmepr approaching this value is unacceptable to solve this problem a new class of ccc using generalized boolean functions and with a column sequence pmepr of at most 2 is proposed in this paper

a construction of ofdm 16 qam sequences having low peak powers using a realization of 16 qam as set addition of two scaled versions of the 4 psk constellation we construct 16 qam sequences having low peak to mean envelope power ratios pmepr from 4 psk golay sequences various upper bounds on the peak envelope powers of these sequences are established transmission using these sequences provides twice as much rate as transmission using complementary golay sequences with a maximum pmepr of 3 6 5 56 db

new bounds and optimal binary signature sets part ii aperiodic total squared correlation we derive new bounds on the aperiodic total squared correlation atsc of binary antipodal signature sets for any number of signatures k and any signature length l we then present optimal designs that achieve the new bounds for several k l cases as interesting arguably side results we show that individual maximal merit factor sequences for example barker sequences are single user atsc optimal while neither the familiar gold nor the kasami set designs are atsc optimal in general the atsc optimal signature set designs provided in this work are in this sense better suited for asynchronous and or multipath code division multiplexing applications

a note on the cross correlation of costas permutations we build on the work of drakakis et al 2011 on the maximal cross correlation of the families of welch and golomb costas permutations in particular we settle some of their conjectures more precisely we prove two results first for a prime p ge 5 the maximal cross correlation of the family of the varphi p 1 different welch costas permutations of 1 ldots p 1 is p 1 t where t is the smallest prime divisor of p 1 2 if p is not a safe prime and at most 1 p 1 2 otherwise here varphi denotes euler s totient function and a prime p is a safe prime if p 1 2 is also prime second for a prime power q ge 4 the maximal cross correlation of a subfamily of golomb costas permutations of 1 ldots q 2 is q 1 t 1 if t is the smallest prime divisor of q 1 2 if q is odd and of q 1 if q is even provided that q 1 2 and q 1 are not prime and at most 1 q 1 2 otherwise note that we consider a smaller family than drakakis et al our family is of size varphi q 1 whereas there are varphi q 1 2 different golomb costas permutations the maximal cross correlation of the larger family given in the tables of drakakis et al is larger than our bound for the smaller family for some q

new optimal z complementary code sets based on generalized paraunitary matrices the concept of paraunitary pu matrices arose in the early 1990 s in the study of multi rate filter banks these matrices have found wide applications in cryptography digital signal processing and wireless communications existing pu matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice motivated by this for the first time we introduce a novel concept called z paraunitary zpu matrix whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value we show that there exists an equivalence between a zpu matrix and a z complementary code set when the latter is expressed as a matrix with polynomial entries furthermore we investigate some important properties of zpu matrices which are useful for the extension of matrix sizes and sequence lengths we propose a new construction framework for optimal zpu matrices which includes existing pu matrices as special cases finally we give the enumeration formula for the constructed z complementary sequences from the optimal zpu matrices

new constructions of general qam golay complementary sequences a construction of general quadrature amplitude modulation qam golay complementary sequences based on quadrature phase shift keying golay davis jedwab sequences gdj sequences is described existing constructions of 16 and 64 qam golay sequences are extended to 4q qam sequences of length 2m for q 1 m 2 this construction gives m 1 42 q 1 m 1 4 q 1 2q 1 m 2 4 m 1 golay complementary sequences a previous offset pair enumeration conjecture for 64 qam golay sequences is proved as a special case of the enumeration for 4q qam golay sequences when used for orthogonal frequency division multiplexing signals the peak to mean envelope power ratio upper bound is shown to be 6 2q 1 2q 1 approaching 6 as the qam constellation size increases

two dimensional synchronization patterns for minimum ambiguity a number of closely related combinatorial problems corresponding to specific assumptions about the type of time frequency sequence which may be appropriate in a particular application are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two dimensional correlation function the current state of knowledge concerning each of these problems is summarized it is hoped that more general constructions may be found leading to larger families of solutions as well as better computational algorithms for finding individual solutions which may lie outside of the general families

on certain sets of polyphase sequences with sparse and highly structured zak and fourier transforms this paper describes a km2 m k q m km z zak space construction of zero correlation zone polyphase sequence sets of sequence length km3 and set size km with all zero cross correlation the construction includes the sets with an m 1 point and t2m 1 point zero autocorrelation zone where t2 is an arbitrary nontrivial factor of m all sequences in these sets have sparse highly structured semipolyphase finite zak transforms with constant nonzero magnitude at m points and zero magnitude at selectable km3 m points and sparse semipolyphase km3 point discrete fourier transforms with constant nonzero magnitude at m2 points and zero magnitude at selectable km3 m2 points

near complementary sequences with low pmepr for peak power control in multicarrier communications new families of near complementary sequences are presented for peak power control in multicarrier communications a framework for near complementary sequences is given by an explicit boolean expression and an equivalent matrix structure the framework transforms seed pairs to near complementary sequences by the aid of golay complementary sequences new families of near complementary sequences of various lengths and pmepr 4 are then presented where the sequences are constructed by the framework employing the seeds of shortened and extended golay complementary pairs the families present in a constructive way a large number of sequences of pmepr 4 for the lengths 100 of 24 28 30 34 36 48 56 60 62 66 68 72 and 96 where no golay pairs have been reported the sequence families can find potential applications for peak power control requiring codewords or sequences of various lengths as well as low peak to mean envelope power ratio pmepr

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

construction of orthogonal and nearly orthogonal designs for computer experiments this paper presents new infinite families of orthogonal designs for computer experiments in cases where orthogonal designs cannot exist we construct alternative nearly orthogonal designs our designs can accommodate many factors and a large set of levels no iterative computer search is required to build up the desired orthogonal designs we develop and use new infinite classes of periodic golay pairs

constructions of quasi complementary sequence sets associated with characters an boldsymbol m boldsymbol k boldsymbol n delta max quasi complementary sequence set qcss is referred to as a set of boldsymbol m 2 d matrices of order boldsymbol k times boldsymbol n with periodic tolerance delta max in a multicarrier code division multiple access mc cdma communication system the set size boldsymbol m of a qcss is equal to the maximum number of users it can support and the periodic tolerance delta max determines the interference performance for the application of a qcss it is desirable that the set size should be as large as possible and the periodic tolerance should be as small as possible in this paper a framework of a periodic qcss is proposed from additive and multiplicative characters associated with a specific integer set it is then discovered that the parameters of the obtained qcss are determined by the employed integer set from this discovery new classes of periodic qcsss with large set sizes and low periodic tolerances are constructed and associated with some known integer sets

a complete description of golay pairs for lengths up to 100 in his 1961 paper marcel golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a 2 6 problem andres in his 1977 master s thesis developed an algorithm which reduced this to a 2 n 2 1 search and investigated lengths up to 58 for existence of pairs in this paper we describe refinements to this algorithm enabling a 2 n 2 5 search at length 82 we find no new pairs at the outstanding lengths 74 and 82 in extending the theory of composition we are able to obtain a closed formula for the number of pairs of length 2 k n generated by a primitive pair of length n combining this with the results of searches at all allowable lengths up to 100 we identify five primitive pairs all others pairs of lengths less than 100 may be derived using the methods outlined

a new construction of 16 qam golay complementary sequences we present a new construction of 16 qam golay sequences of length n 2 sup m the number of constructed sequences is 14 12m m 2 4 sup m 1 when employed as a code in an orthogonal frequency division multiplexing ofdm system this set of sequences has a peak to mean envelope power ratio pmepr of 3 6 by considering two specific subsets of these sequences we obtain new codes with pmepr bounds of 2 0 and 2 8 and respective code sizes of 2 2m m 2 4 sup m 1 and 4 4m m 2 4 sup m 1 these are larger than previously known codes for the same pmepr bounds

square array antennas based on hadamard difference sets a regular method for synthesizing a planar aperiodic thinned array antenna aa with a low peak sidelobe level is suggested it is based on using specific combinatorial constructions noncyclic difference sets dss the method uses the fact that when the elements of an equiamplitude aa are arranged according to a ds law its power pattern takes constant value in the net of uniformly located space points in the sidelobe region and this value is less than where is the element number in distinction to the method using cyclic dss see leeper 1999 which enables one to build planar aas only on rectangular grids with co prime sidelengths the represented method omits such a constraint the most important class of the noncyclic 2 d dss is represented by the sets of hadamard type sets based on such sets rectangular and square aperiodic roughly half filled aas can be built here the numerical results obtained for the square aas with the element number in the array up to 300 are presented

2 d quasi m arrays and gold code arrays two dimensional quasi maximal area arrays quasi m arrays are proposed these quasi m arrays are so named because their cyclic correlation properties are very close to those of the m arrays these arrays are generated by modulo 2 addition of maximal length sequences the cyclic autocorrelation of any quasi m array is close to the delta function in addition the cyclic cross correlation is small compared with the cyclic autocorrelation peak two dimensional gold code arrays generated by the same construction method are also studied correlation properties of these gold code arrays are similar to those of the quasi m arrays the gold code arrays provide families of arrays in which any two arrays have the bound on their cyclic cross correlation these arrays are also shown to have the quasi orthogonal property

doppler resilient golay complementary waveforms we describe a method of constructing a sequence pulse train of phase coded waveforms for which the ambiguity function is free of range sidelobes along modest doppler shifts the constituent waveforms are golay complementary waveforms which have ideal ambiguity along the zero doppler axis but are sensitive to nonzero doppler shifts we extend this construction to multiple dimensions in particular to radar polarimetry where the two dimensions are realized by orthogonal polarizations here we determine a sequence of two by two alamouti matrices where the entries involve golay pairs and for which the range sidelobes associated with a matrix valued ambiguity function vanish at modest doppler shifts the prouhet thue morse sequence plays a key role in the construction of doppler resilient sequences of golay complementary waveforms

bounds and constructions of disjoint sets of distinct difference sets an i j ddd is a set of i disjoint sets of distinct difference sets each having j elements a number of constructions are given upper and lower bounds on the maximal element in a ddd disjoint distinct difference set are given it is shown that regular ddd sets exist for i or approximately 4j

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

new bounds for the sizes of radar arrays improved upper bounds for the size of radar arrays are found by using the window method new general constructions and computer searched examples are presented the radar array problem is generalized to include arrays with sidelobes greater than 1

a low frequency model for dynamic motion in pre stressed incompressible elastic structures an asymptotic one dimensional theory with minimal essential parameters is constructed to help elucidate two dimensional low frequency dynamic motion in a pre stressed incompressible elastic plate in contrast with the classical theory the long wave limit of the fundamental mode of antisymmetric motion is non zero the occurrence of an associated quasi front therefore offers considerable deviation from the classical case moreover the presence of pre stress makes the plate stiffer and thus may preclude bending in the classical sense discontinuities on the associated leading order wavefronts are smoothed by deriving higher order theories both quasi fronts are shown to be either receding or advancing but of differing type the problems of surface and edge loading are considered and in the latter case a specific problem is formulated and solved to illustrate the theory in the case of antisymmetric motion and an appropriate form of pre stress it is shown that the leading order governing equation for the mid surface deflection is essentially that of waves propagating along an infinite string a higher order equation for which is derived

on timoshenko reissner type theories of plates and shells abstract linear tr theories timoshenko reissner theories of isotropic plates and shells are discussed these theories take into account the transversal shear deformation and rotation inertia the main subject under consideration is the construction of these theories by the asymptotic method and the related error estimates for static and dynamic problems in the dynamic case a method is suggested for the extension of the range of applicability of the tr theory

acquisition sequences in ppm communications corresp in pulse position modulation ppm communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission this sequence must have ppm structure one pulse per frame and desirable autocorrelation properties for its detection the problem of finding aperiodic ppm acquisition sequences having the minimum possible autocorrelation for all off shifted positions is investigated sequences with the maximum possible number of frames have been found up to frame size 15 examples are given for every frame length up to 88 and powers of two up to 1024 an interesting relation between the ppm sequence problem costas and sonar arrays and golomb s ruler is explored

two dimensional perfect binary arrays with 64 elements perfect binary arrays can exist for numbers of elements that are even square numbers two dimensional 2 d perfect binary arrays are 4 16 36 and 144 elements are known perfect binary arrays with 64 elements can be constructed for three or more dimensions here two dimensional binary arrays with 64 elements are examined the results of computer search for symmetric binary arrays with 64 elements are presented in the form of two 2 d perfect binary arrays with sizes 8 8 and 4 16 applications of these perfect binary arrays are in 2 d synchronization time frequency coding and coding loudspeaker fields

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

synthesis of power efficient multitone signals with flat amplitude spectrum it is shown that generally any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 db the previously proposed shapiro rudin sequences are representatives of a much larger family of binary golay complementary sequences numerical investigations show that the values of the crest factors obtained by applying complementary sequences binary or polyphase are between 5 and 6 db regardless of the number of tones

periodic complementary binary sequences existence conditions and recursive construction procedures for sets of periodic complementary binary sequences are given relationships to sets of aperiodic complementary binary sequences and to perfect binary arrays whose two dimensional periodic autocorrelation function is a delta function are noted the connections of periodic complementary binary sequences and difference families are given sets of periodic complementary binary sequences which result from computer search are presented a diagram showing what is currently known about the existence of periodic complementary binary sequences with p

on cosets of the generalized first order reed muller code with low pmepr golay sequences are well suited for use as codewords in orthogonal frequency division multiplexing ofdm since their peak to mean envelope power ratio pmepr in q ary phase shift keying psk modulation is at most 2 it is known that a family of polyphase golay sequences of length 2m organizes in m 2 cosets of a q ary generalization of the first order reed muller code rmq 1 m in this paper a more general construction technique for cosets of rm q 1 m with low pmepr is established these cosets contain so called near complementary sequences the application of this theory is then illustrated by providing some construction examples first it is shown that the m 2 cosets of rmq 1 m comprised of golay sequences just arise as a special case second further families of cosets of rmq 1 m with maximum pmepr between 2 and 4 are presented showing that some previously unexplained phenomena can now be understood within a unified framework a lower bound on the pmepr of cosets of rmq 1 m is proved as well and it is demonstrated that the upper bound on the pmepr is tight in many cases finally it is shown that all upper bounds on the pmepr of cosets of rmq 1 m also hold for the peak to average power ratio papr under the walsh hadamard transform wht

a systematic construction for radar arrays the radar array problem arises from the need to design frequency hopping sequences with small out of phase autocorrelations it assumes the reflected signals have negligible doppler shifts so the correlations are calculated along the time axis only in this correspondence a systematic construction for radar arrays is provided by means of homogeneous uniform difference matrices a systematic construction for properly centered permutation matrices a special kind of homogeneous uniform difference matrices is also provided which partially solves the open problems posed by zhang and tu

complementary sequences for isi channel estimation a merit factor based on the sequence autocorrelation function whose minimization leads to the reduction in the cramer rao lower bound crlb for the variance of two sided intersymbol interference isi channel estimation is introduced pairs of binary pilot symbol sequences a preamble and a postamble for channel estimation are jointly designed to minimize this merit factor given that the number of channel taps is l and the length of a pilot symbol sequence is n l 1 where n spl ges l we distinguish between the case when n is even and the case when it is odd for even n we show that complementary sequences not only minimize the merit factor but also the crlb for a subset of odd n we construct almost complementary periodic sequence pairs that minimize the merit factor the optimal pilot symbol block signaling requires alternating between two in most cases different binary sequences that form the merit minimizing pair

multiple binary zcz sequence sets with good cross correlation property based on complementary sequence sets in this paper two types of multiple binary zero correlation zone zcz sequence sets are constructed 1 each set is a binary 2n 1zcz 2n zcz zcz sequence set which is one of the best cases in the known constructions 2 among all the sets the sequences still possess good cross correlation property within the zone of length z zcz in particular the first type sequence sets have a common zero correlation zone of length z which solves the previous research problem these multiple binary zcz sequence sets are suitable for multiuser environments

on three dimensional edge waves in semi infinite isotropic plates subject to mixed face boundary conditions this paper is concerned with the propagation of three dimensional waves localized near the edge of a semi infinite elastic plate subject to mixed face boundary conditions in the linear isotropic case it is shown that the problem is closely related to that of rayleigh surface wave propagation along the free surface of the corresponding half space the cut off frequencies of the analyzed edge waves coincide with the natural frequencies of the associated cross sectional semi infinite strip it is also demonstrated that the eigenspectrum of a rectangular rod can be expressed in terms of the considered three dimensional waves the results are then generalized to a prestressed isotropic incompressible material it is noted that the density of the edge wave spectrum is strongly influenced by the prestress it is illustrated that the areas of negative group velocity may exist for large primary deformation long wave asymptotic expansions in the vicinity of the cut off frequencies are presented

symmetric golomb squares inspection of optimum golomb squares found by exhaustive computer search shows some are symmetric with respect to diagonal reflection this suggests searching for such symmetric golomb squares might be an efficient way to find good squares in this correspondence we find the best symmetric n spl times n golomb squares for n spl les 22 some appear to be the best known

asymptotic long wave models for a pre stressed elastic layer with elastically restrained boundaries abstract long wave dispersion phenomena is investigated in respect of a pre stressed incompressible elastic layer subject to elastically restrained boundary conditions erbc such conditions can be treated as a generalisation of classical free and fixed face boundary conditions allowing investigating of the transition between the neumann and dirichlet statements of the problem symmetric elastically restrained boundary conditions are introduced followed by both a numerical investigation and a multi parameter asymptotic analysis of the dispersion relations all possible asymptotic regimes are grouped into classes based on the magnitude of the associated restraint parameter a long wave low frequency model is developed to describe motion associated with the fundamental modes for small values of the restraint parameters four high frequency models are developed describing asymptotic regimes connected with vibration within the vicinity of the thickness resonances

a tighter correlation lower bound for quasi complementary sequence sets levenshtein improved the famous welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation following levenshtein s idea a new correlation lower bound for quasi complementary sequence sets qcsss over the complex roots of unity is proposed in this paper the derived lower bound is shown to be tighter than the welch bound for qcsss when the set size is greater than some value the conditions for meeting the new bound with equality are also investigated

golomb rectangles as folded rulers a correspondence between two dimensional golomb rectangles and one dimensional golomb rulers is given results are translated from rulers to rectangles the extension of these results to an arbitrary number of dimensions is given a new bound is developed on the number of ones in a golomb array of any dimension some new optimum golomb squares rectangles and higher dimensional arrays are given

a new weight vector for a tighter levenshtein bound on aperiodic correlation the levenshtein bound on aperiodic correlation which is a function of the weight vector is tighter than the welch bound for sequence sets over the complex roots of unity when m 4 and n 2 where m denotes the set size and n the sequence length although it is known that the tightest levenshtein bound is equal to the welch bound for m 1 2 it is unknown whether the levenshtein bound can be tightened for m 3 and levenshtein in his paper published in 1999 postulated that the answer may be negative a new weight vector is proposed in this paper which leads to a tighter levenshtein bound for m 3 n 3 and m 4 n 2 in addition the explicit form of the weight vector which is derived by relating the quadratic minimization to the chebyshev polynomials of the second kind in levenshtein s paper is given interestingly this weight vector also yields a tighter levenshtein bound for m 3 n 3 and m 4 n m a fact not noticed by levenshtein

correlation and set size bounds of complementary sequences with low correlation zone the correlation lower bounds as well as the set size upper bounds of low correlation zone complementary sequences are presented in this paper they can be treated as an extension of tang fan matsufuji bounds in and which considered only the conventional non complementary low correlation zone sequence sets

harmonic maps from noncompact riemannian manifolds with non negative ricci curvature outside a compact set in this paper we prove the uniqueness and existence of harmonic maps of finite energy from a complete noncompact riemannian manifold m g with sobolev constant s2 m 0 and ricci curvature ric m 0 outside some compact subset into a complete manifold of nonpositive curvature or a regular ball in particular we prove the uniqueness and existence of bounded harmonic functions on m g

genetic search for golomb arrays genetic search with a decision level chromosome is used to search efficiently for golomb 1982 arrays a golomb array a is a binary array with three values for its discrete autocorrelation function m the number of ones in a for no offset 1 when there is partial overlap and 0 otherwise in one dimension a is known as a golomb ruler the method yields improvement because the genetic search considers only feasible solutions in the most likely portion of the search space each chromosome bit represents a decision to place a one in an iterative construction the representation includes all possible arrays since the chromosome bits represent binary decisions in the search space genetic operations such as crossover and mutation always result in feasible descendent chromosomes experimental results include comparison to previously known search methods and several new arrays these results indicate that the proposed search is significantly more efficient than prior methods

on interfacial waves in pre stressed layered incompressible elastic solids interfacial waves along the plane boundary between two pre stressed incompressible elastic solids are considered one of the solids is a half space while the other has arbitrary uniform thickness the principal axes of the underlying pure homogeneous deformation in the two solids are aligned with one axis normal to the interface for propagation along an in plane principal axis the dispersion equation is derived in respect of a general strain energy function conditions on the pre strain pre stress and material parameters that ensure the existence of a unique interfacial wavespeed at low frequencies are obtained and it is shown that in special circumstances non dispersive waves can exist at the low frequency limit asymptotic results at the high frequency limit are also obtained for the case of equibiaxial pre strain more specific conditions are derived for the existence of interfacial waves at the low and high frequency asymptotes and these provide information on the existence of waves for the whole frequency range a particular feature of the structure considered is that it may act as a mechanical filter in different frequency regimes depending on the pre strain pre stress and material parameters when the wavespeed vanishes the dispersion equation reduces to a bifurcation equation solutions of which define states of stress and deformation which form boundaries of the region of stability of the underlying state of stress and deformation in the two materials for given material properties the bifurcation equation is examined separately and an explicit bifurcation criterion is given for equibiaxial deformations the results are illustrated graphically by considering several numerical examples based on a certain class of strain energy functions which includes the neo hookean strain energy function the results highlight low and high frequency features and demonstrate the influence of pre stress and deformation on the multiplicity of propagating modes

on aperiodic and periodic complementary binary sequences we give direct and recursive constructions for aperiodic and periodic complementary sequences using these constructions many missing entries in the table of bomer and antweiler 1990 can be filled

perfect three level and three phase sequences and arrays introduces construction methods for synthesizing new classes of perfect sequences and arrays time discrete sequences and arrays are perfect if their periodic autocorrelation function sidelobes are zero the construction of perfect three level and three phase sequences is performed in two steps in the first step a maximal length shift register sequence with elements in gf q is built for a length of g sup m spl minus 1 where q is a prime power and m is a positive integer in the second step a sequence is constructed by mapping the elements of the shift register sequence to 1 b sub 1 or b sub 2 two real numbers b sub 1 and b sub 2 are determined such that the sequence becomes perfect and has high energy efficiency the phase values for complex numbers b sub 1 and b sub 2 with magnitude 1 are given for perfect three phase sequences it is shown that the phase values of b sub 1 and b sub 2 tend for growing lengths to 2 spl pi 3 and 4 spl pi 3 a different similar synthesizing method starts with legendre sequences the construction of perfect three level and three phase arrays is performed by several methods which make use of the new respective sequences

a non local asymptotic theory for thin elastic plates the three dimensional dynamic non local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size the integral constitutive relations incorporating the variation of an exponential non local kernel across the thickness are adopted long wave low frequency approximations are derived for both bending and extensional motions boundary layers specific for non local behaviour are revealed near the plate faces it is established that the effect of the boundary layers leads to the first order corrections to the bending and extensional stiffness in the classical two dimensional plate equations

two constructions of asymptotically optimal quasi complementary sequence sets an m k n delta mathrm max quasi complementary sequence set qcss is referred to as a set of m two dimensional matrices of size k times n with maximum periodic correlation magnitude delta mathrm max it can be applied to a multi carrier code division multiple access communication system to achieve low interference performance compared with perfect complementary sequence sets qcsss with maximum periodic correlation magnitudes achieving or asymptotically achieving the correlation lower bounds have the advantage of supporting more users in this paper two constructions of periodic qcsss from additive characters and multiplicative characters of finite fields are developed in the first construction new qcsss with constituent sequence length n p are proposed by using cyclic classes where p is a prime in the second construction qcsss with constituent sequence length n q 1 and n r 2 1 are presented by employing almost difference sets and special sets proposed by katz respectively where q 5 is an odd prime power and r is a prime power notably the parameters of qcsss derived from the second construction are flexible and have not been covered in the literature in addition all the proposed periodic qcsss are asymptotically optimal with respect to the correlation lower bounds

n shift cross orthogonal sequences n shift cross orthogonal sequences and a complete complementary code derived from them are defined and discussed a general method for generating this code is also discussed a synchronous multiple user spread spectrum multiple system is proposed that uses n shift cross orthogonal sequences

binary odd periodic complementary sequences a pair of binary sequences is called complementary if the sum of their aperiodic autocorrelation functions is zero except for zero shift such sequences are known for relatively few lengths this correspondence therefore introduces pairs of binary odd periodic complementary sequences which can be constructed using q ary m sequences for many more lengths

two dimensional patterns with distinct differences constructions bounds and maximal anticodes a two dimensional 2 d grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope these configurations are known to have many applications such as radar sonar physical alignment and time position synchronization rather than restricting dots to lie in a square or rectangle as previously studied we restrict the maximum distance between dots of the configuration the motivation for this is a new application of such configurations to key distribution in wireless sensor networks we consider configurations in the hexagonal grid as well as in the traditional square grid with distances measured both in the euclidean metric and in the manhattan or hexagonal metrics we note that these configurations are confined inside maximal anticodes in the corresponding grid we classify maximal anticodes for each diameter in each grid we present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes our bounds settle in the negative a question of golomb and taylor on the existence of honeycomb arrays of arbitrarily large size we present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various 2 d shapes such as anticodes by considering periodic configurations with distinct differences in the square grid

16 qam almost complementary sequences with low pmepr a pair of sequences is said to be an almost complementary pair acp if they have zero aperiodic autocorrelation sums except at only one position over all the positive negative time shifts having correlation property very close to that of golay complementary pairs gcps acps may be used as an alternative to gcps in many applications in communications and radar for high rate code keying ofdm communication we construct novel 16 qam acps from three new classes of quadratic offsets leading to three large sets of 16 qam almost complementary sequences with maximum peak to mean envelope power ratio pmepr of 2 4

golomb rectangles there are a number of communications problems involving two dimensional arrays with constrained correlation functions golomb s two classes of radar arrays and sonar arrays are examined improved bounds optimal cases and computational procedures are reported

on the existence of square dot matrix patterns having a specific three valued periodic correlation function the author examines square matrices of size n containing dot patterns satisfying the following two restrictions 1 each column contain precisely one dot and 2 if the pattern is moved around over a plane tied by the same pattern when in all positions except the home position there is at most one overlap in dots from differing viewpoints there matrices are the characteristic functions of either a certain class of relative difference sets or else a select subset of bent functions also the existence of such an n n matrix implies the existence of a finite projective plane of order n a family of constructions for such matrices is available when n is prime a polynomial equation characterizing such matrices and resembling the hall polynomial equation of cyclic difference sets is presented analogs of known existence tests for cyclic difference sets are then applied to rule out existence for most nonprime values of n it is shown how such patterns can be used to provide hopping patterns for a frequency hopped multiple access system

a long wave model for the surface elastic wave in a coated half space the paper deals with the three dimensional problem in linear isotropic elasticity for a coated half space the coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long wave limit an explicit model is derived for the surface wave using the perturbation technique along with the theory of harmonic functions and radon transform the model consists of three dimensional quasi static elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two dimensional hyperbolic equation singularly perturbed by a pseudo differential or integro differential operator the latter equation governs dispersive surface wave propagation whereas the elliptic equations describe spatial decay of displacements and stresses as an illustration the dynamic response is calculated for impulse and moving surface loads the explicit analytical solutions obtained for these cases may be used for the non destructive testing of the thickness of the coating and the elastic moduli of the substrate

dispersion phenomena in symmetric pre stressed layered elastic structures the dispersion relation associated with a symmetric three layer structure composed of compressible pre stressed elastic layers is derived this mathematically elaborate transcendental equation gives phase speed as an implicit function of wave number numerical solutions are established to show a wide range of dispersion behaviour which is delicately dependent on the material parameters and pre stress in each layer particularly interesting behaviour is observed within the short wave high wave number regime with six possible cases of short wave liming behaviour shown possible within each of these a short wave asymptotic analysis is carried out resulting in a set of approximations which provide explicit relationships between phase speed and wave number it is envisaged that these approximations may prove helpful to approximate numerical truncation errors associated with impact response as well as providing excellent first approximations for particularly numerically challenging sets of material parameters

boundary regularity and the dirichlet problem for harmonic maps in a previous paper 10 we developed an interior regularity theory for energy minimizing harmonic maps into riemannian manifolds in the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed dirichlet boundary condition we show that such maps are regular in a full neighborhood of the boundary assuming appropriate regularity on the manifolds the boundary and the data the reader may refer to theorem 2 7 for a statement of the precise result it is not surprising that the boundary regularity is actually stronger than the partial regularity we obtained for the interior this is due to the fact that there are no nontrivial smooth harmonic maps from hemispheres s which map the boundary s 9s to a point i j n 2 and is analogous to the fact that in certain cases we were able to obtain complete regularity in the interior many authors have worked on boundary regularity for this general type of problem we mention hildebrandt and widman 5 and hamilton 4 as having obtained important results specifically for harmonic maps morrey had obtained the boundary regularity for domain dimension n 2 in conjunction with his investigation of the plateau problem in riemannian manifolds 8 in 3 of this paper we observe that the direct method gives solvability of the dirichlet problem under reasonable hypotheses on the manifolds we give as an application an amusing proof of a theorem of sacks and uhlenbeck 9 on the existence of minimal 2 spheres representing the second homotopy group of a manifold the same method gives smooth harmonic representations for k n for a certain class of manifolds n these are characterized by the nonexistence of lower dimensional harmonic spheres whose homogeneous extensions are minimal see proposition 3 4 in the last section of the paper we discuss approximation of l maps by smooth maps we give a simple example of an l map from the three dimensional ball to the two sphere which is not an l limit of continuous maps we