golay complementary sequence sets with large zero correlation zones zero correlation zone zcz sequence sets and golay complementary sets gcss have different correlation properties and hence have different engineering applications a number of constructions of zcz sequence sets and gcss have been proposed respectively in the literature in addition some zcz sequence sets can be constructed from mutually orthogonal gcss in this paper the relationship between gcss and zcz sets is discovered further we propose a new type of sequence sets which are zcz sequence sets and also gcss they are called the golay zcz sequence sets in this paper therefore they have low peak to average power ratios when employed in ofdm systems due to the good autocorrelation properties of gcss besides the golay zcz sets possess zero autocorrelations and cross correlations within their zcz and hence have the potential application to synchronization furthermore a construction of golay zcz sequence family with flexible set sizes various sequence lengths and large zcz widths is proposed in this paper

comments on a new construction of 16 qam golay complementary sequences and extension for 64 qam golay sequences for original article by c v chong see ibid vol 49 no 11 p 2953 2959 nov 2003 some corrections are given for the sequence pairing descriptions of 16 qam golay complementary sequences in chong venkataramani and tarokh s paper together with a related correction for lee and golomb s 64 qam golay sequence construction lee and golomb obtained 496 808 and 976 offset pairs for length 2m 64 qam golay sequences m 2 3 4 we obtained 724 972 and 1224 offset pairs adding w 1 to case iii in lee and golomb s construction gives some additional offset pairs others are new and exist for m ges 3 only descriptions of new offset pairs and enumeration for all first order offset pairs are proposed as conjectures an example is given to show that there exist other 64 qam golay sequences not within this construction

discrete fourier transform of boolean functions over the complex field and its applications in this paper the discrete fourier transform dft of boolean functions over the complex field is introduced and the locations of zero valued fourier spectrum are studied then a fourier spectral characterization of correlation immune and resilient boolean functions is investigated it is shown that a boolean function f is m th order correlation immune if and only if the fourier spectrum of f under any permutation of variables or the equivalence class of f defined by golomb in 1959 vanishes at a specified location this is an analog of using walsh hadamard spectra to characterize correlation immunity of the boolean functions in particular if f is a symmetric function f is correlation immune if and only if its fourier spectrum vanishes at a specified location similarly zero valued fourier spectrum can also be used to characterize resilient functions the application of the fourier spectral analysis on studying the peak to mean envelope power ratio of the sequences is also addressed

on the pmepr of binary golay sequences of length 2 n in this paper some questions on the distribution of the peak to mean envelope power ratio pmepr of standard binary golay sequences are solved for n odd we prove that the pmepr of each standard binary golay sequence of length 2n is exactly 2 and determine the location s where peaks occur for each sequence for n even we prove that the envelope power of such sequences can never reach 2n 1 at time points t v 2u 0 v 2u v u n we further identify eight sequences of length 24 and eight sequences of length 26 that have pmepr exactly 2 and raise the question whether asymptotically it is possible for standard binary golay sequences to have pmepr less than 2 where 0

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

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

schemas sur les categories abeliennes monoidales symetriques et faisceaux quasi coherents resume soit x un schema sur une categorie abelienne monoidale symetrique c 1 verifiant certaines conditions dans cet article nous developpons la theorie de la categorie derivee d o x qcoh des faisceaux quasi coherents sur x ou x n est pas necessairement noetherien en particulier nous montrons les deux resultats suivants sur la categorie d o x qcoh 1 la categorie d o x qcoh est munie d un produit tensoriel derive et un hom interne et 2 soit x la plus petite sous categorie triangulee contenant tous les objets j m ou j u x est une immersion ouverte avec u affine et m d o u qcoh alors x d o x qcoh

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

shared autocorrelation property of sequences due to the low peak to mean envelope power ratio pmepr of golay sequences together with their connection to generalized reed muller codes many authors have proposed using golay sequences as codewords in orthogonal frequency division multiplexing ofdm golay sequences that unexpectedly share the same aperiodic autocorrelation function can be used to construct longer golay sequences we study the shared autocorrelation property of general sequences with the ultimate goal of using those results to find other low power sequences in this paper we provide several new constructions of families of pairs of sequences with the shared autocorrelation property that enable us to explain nearly all of the binary shared autocorrelation property for sequences of lengths up to 24

on the computation and reduction of the peak to average power ratio in multicarrier communications for any code c defined over an equal energy constellation it is first shown that at any time instance the problem of determining codewords of c with high peak to average power ratios papr in a multicarrier communication system is intimately related to the problem of minimum distance decoding of c subsequently a method is proposed for computing the papr by minimum distance decoding of c at many points of time moreover an upper bound on the error between this computed value and the true one is derived analogous results are established for codes defined over arbitrary signal constellations as an application of this computational method an approach for reducing the papr of c proposed by jones and wilkinson 1996 is revisited this approach is based on introducing a specific phase shift to each coordinate of all the codewords where phase shifts are independent of the codewords and known both to the transmitter and the receiver we optimize the phase shifts offline by applying our method for computing the papr for the coding scenario proposed by the etsi bran standardization committee reductions of order 4 5 db can be freely obtained using the computed phase shifts examples are provided showing that most of the gain is preserved when the computed optimal phase shifts are rounded to quantenary phase shift keying psk 8 psk and 16 psk type phase shifts

complementary sets of non power of two length for peak to average power ratio reduction in ofdm golay complementary sequences and complementary sets have been proposed to deal with the high peak to average power ratio papr problem in orthogonal frequency division multiplexing ofdm system the existing constructions of complementary sets based on generalized boolean functions are limited to lengths which are powers of two in this paper we propose novel constructions of binary and nonbinary complementary sets of non power of two length regardless of whether or not the length of the complementary set is a power of two its papr is still upper bounded by the size of the complementary set therefore the constructed complementary sets can be applied in practical ofdm systems where the number of used subcarriers is not a power of two in addition while the binary golay complementary pairs exist only for limited lengths the constructed binary complementary sets of size 4 exist for more lengths with papr at most 4

reed solomon and simplex codes for peak to average power ratio reduction in ofdm new schemes for peak to average power ratio reduction in orthogonal frequency division multiplexing ofdm systems are proposed reed solomon rs and simplex codes are employed to create a number of candidates from which the best are selected thereby in contrast to existing approaches the codes are arranged over a number of ofdm frames rather than over the carriers hence a combination of the principles of multiple signal representation with selection as done in selected mapping and the use of channel coding is present in particular in multiple antenna transmission the proposed schemes do not cause any additional delay but due to the utilization of the dimension space additional gains can be achieved moreover the schemes are very flexible due to the selection step any criterion of optimality can be taken into account besides multiple antenna transmission packet transmission is briefly considered which moreover covers the appealing similarities with incremental redundancy check schemes in automatic repeat request arq applications and with decoding of codes transmitted over the erasure channel the performance of the schemes is using some approximations derived analytically and is covered by numerical results that are in very good agreement with the theory significant gains can be achieved with these very flexible and versatile methods

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

new sufficient conditions for linear feedback closed loop stackelberg strategy of descriptor systems this paper is concerned with the derivation of linear feedback closed loop stackelberg lfcls strategies for a class of continuous time two person nonzero sum differential games characterized by linear descriptor systems and the quadratic cost functionals compared with existing results new sufficient conditions for the existence of a lfcls strategy are obtained under less restrictive conditions furthermore from the results of this paper the authors also arrive at some conclusions about the linear quadratic closed loop nash game for continuous time descriptor systems these conclusions are distinguished from those of the linear quadratic closed loop nash game for state space systems

novel 16 qam and 64 qam near complementary sequences with low pmepr in ofdm systems in this paper we first propose a novel construction of 16 quadrature amplitude modulation qam near complementary sequences with low peak to mean envelope power ratio pmepr in orthogonal frequency division multiplexing ofdm systems the proposed 16 qam near complementary sequences can be constructed by utilizing novel nonlinear offsets where the length of the sequences is n 2 m the family size of the newly constructed 16 qam near complementary sequences is 8 times m 2 times 4 m 1 and the pmepr of these sequences is proven to satisfy pmepr 2 4 thus the proposed construction can generate a number of 16 qam near complementary sequences with low pmepr resulting in the improvement of the code rate in ofdm systems furthermore we also propose a novel construction of 64 qam near complementary sequences with low pmepr which is the first proven construction of 64 qam near complementary sequences the pmeprs of two types of the proposed 64 qam near complementary sequences are proven to satisfy that pmepr 3 62 or pmepr 2 48 respectively the family size of the newly constructed 64 qam near complementary sequences is 64 times m 2 times 4 m 1

complementary sets generalized reed muller codes and power control for ofdm the use of error correcting codes for tight control of the peak to mean envelope power ratio pmepr in orthogonal frequency division multiplexing ofdm transmission is considered in this correspondence by generalizing a result by paterson it is shown that each q phase q is even sequence of length 2m lies in a complementary set of size 2k 1 where k is a nonnegative integer that can be easily determined from the generalized boolean function associated with the sequence for small k this result provides a reasonably tight bound for the pmepr of q phase sequences of length 2 m a new 2h ary generalization of the classical reed muller code is then used together with the result on complementary sets to derive flexible ofdm coding schemes with low pmepr these codes include the codes developed by davis and jedwab as a special case in certain situations the codes in the present correspondence are similar to paterson s code constructions and often outperform them

a systematic framework for the construction of optimal complete complementary codes the complete complementary code ccc that was proposed by suehiro and hatori is a sequence family that is a set of sequence sets with ideal correlation sums numerous studies in the literature show its applications to direct spread code division multiple access ds cdma systems for interchannel interference ici free communication with improved spectral efficiency in this paper we propose a systematic framework for the construction of cccs based on n shift cross orthogonal sequence families n co sfs we show theoretical bounds on the size of n co sfs and cccs and give a set of four algorithms for their generation and extension the algorithms are optimal in the sense that the size of the resultant sequence families achieves theoretical bounds and with the algorithms we can construct an optimal ccc consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence sets we also discuss the family size alphabet size and length of constructible cccs based on the proposed algorithms

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

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

descriptor variable systems and optimal state regulation linear systems of the form e dot x ax bu with e singular are treated it is desired to find a control which drives the system asymptotically to the origin minimizing a quadratic cost functional no restrictions are placed on initial conditions the cost associated with the impulsive behavior of the system is examined as well as existence and uniqueness of the optimal control through a sequence of coordinate transformations it is proven that the optimal control can be found by solving a reduced order riccati equation

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

how do more golay sequences arise in 1999 davis and jedwab gave a direct construction of golay complementary sequences over zopf2 h of length 2 m recently li and chu found 1024 more quaternary golay complementary sequences of length 16 that cannot be obtained by the direct construction using exhaustive computer enumeration it is shown how these sequences arise from interleaving and concatenation of two classes of golay complementary sequences given as an example by davis and jedwab these examples spawn new golay sequences over zopf2 h of length 2m for all h ges 2 and m ges 4

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 descriptor system approach to singular perturbation of linear regulators the relationship between the regulator problem for a singularly perturbed system and the analogous one for a descriptor system is investigated meanwhile a decomposition approach is provided for solution of the linear quadratic regulator problem for singularly perturbed systems this approach is a significant advance over the two stage method

near shannon limit and low peak to average power ratio turbo block coded ofdm in this paper we present an advanced solution for the long standing problem of large peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems although the design of low papr codewords has been extensively studied and the existence of asymptotically good codes with low papr is also proven still no code has been constructed to satisfy all requirements the main goal of the paper is to develop a coding scheme that not only generates low papr codewords but it also performs relatively close to the shannon limit we achieve this goal by implementing a time frequency turbo block coded ofdm in this scheme we design the frequency domain component to have a tightly bounded papr the time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity through comparative performance evaluation we show that utilizing the proposed method we achieve considerable improvement in terms of papr while we slightly loose the performance compared to capacity achieving codes with similar overall block length

on the peak to mean envelope power ratio of phase shifted binary codes the peak to mean envelope power ratio pmepr of a code employed in orthogonal frequency division multiplexing ofdm systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift motivated by some previous designs of phase shifts using suboptimal methods the following question is considered in this paper for a given binary code how much pmepr reduction can be achieved when the phase shifts are taken from a 2h ary phase shift keying 2h psk constellation a lower bound on the achievable pmepr is established which is related to the covering radius of the binary code generally speaking the achievable region of the pmepr shrinks as the covering radius of the binary code decreases the bound is then applied to some well understood codes including nonredundant bpsk signaling bch codes and their duals reed muller codes and convolutional codes it is demonstrated that most presumably not optimal phase shift designs from the literature attain or approach our bound

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

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

efficient numerical procedures for solving closed loop stackelberg strategies with small singular perturbation parameter in this paper the computation of the linear closed loop stackelberg strategies with small singular perturbation parameter that characterizes singularly perturbed systems sps are studied the attention is focused on a new numerical algorithm for solving a set of cross coupled algebraic lyapunov and riccati equations calre it is proven that the new algorithm guarantees the local quadratic convergence a numerical example is solved to show a reduction of the average cpu time compared with the existing algorithm

completions of monoid objects and descent results abstract let c 1 be an abelian closed symmetric monoidal category satisfying certain conditions the purpose of this paper is to prove three descent results for schemes over c 1 that are not necessarily noetherian

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

paraunitary based boolean generator for qam complementary sequences of length 2 k a boolean generator for a large number of standard complementary qam sequences of length 2 k is proposed this boolean generator is derived from the authors earlier paraunitary generator which is based on matrix multiplications both generators are based on unitary matrices in contrast to previous boolean qam algorithms which represent complementary sequences as a weighted sum our algorithm has a multiplicative form any element of a sequence can be generated efficiently by indexing the entries of unitary matrices with the binary representation of the discrete time index which is easily implemented as a binary counter our 1qum based on one qam unitary matrix and 2qum based on two qam unitary matrices algorithms generate generalized case i iii sequences and generalized case iv and v sequences respectively as specified by liu et al in 2013 in addition to many new 2qum sequences the ratio of the numbers of sequences that are generated by our new construction and the previous construction increases with the constellation size for example for a 1024 qam sequence of length 1024 this ratio is 4 4 however if we compare only 2qum sequences to case iv and v sequences this ratio is 267

generalized bent criteria for boolean functions i generalizations of the bent property of a boolean function are presented by proposing spectral analysis with respect to a well chosen set of local unitary transforms quadratic boolean functions are related to simple graphs and it is shown that the orbit generated by successive local complementations on a graph can be found within the transform spectra under investigation the flat spectra of a quadratic boolean function are related to modified versions of its associated adjacency matrix

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

the linear quadratic optimal regulator for descriptor systems in this paper we investigate the linear quadratic optimal regulator problem for the continuous time descriptor system e dot x ax bu where e is in general a singular matrix we solve first a general finite horizon problem by applying the calculus of variations to derive the optimal trajectory of the vector consisting of the concatenated descriptor codescriptor and control vectors from this trajectory the optimal feedback gain relating the control and descriptor variable can be computed by transforming to a coordinate system which can be computed by performing a singular value decomposition of e we derive several riccati differential equations all of which have the same solution this solution gives the optimal cost the steady state optimal feedback gain can be computed by solving an eigenvalue eigenvector problem formulated from the untransformed system parameters in general there does not exist a unique optimal feedback gain but rather the gain is constrained to lie in a linear variety whose dimension is equal to the number of inputs times the rank deficiency of e

generation and correlation architectures of multilevel complementary sets of sequences complementary sets of sequences css are used extensively in many applications as channel estimation and synchronization preamble or as a basic block for the generation of generalized orthogonal go sequences nevertheless binary css exist for very limited lengths while for multilevel css there are fewer limitations in the sequence length this paper presents two modular architectures for the generation and correlation of k multilevel css an algorithm for k 2k k n 0 multilevel css and another for k 3 4 multilevel css in contrast to previous generation algorithms the proposed architectures reduce the number of computations needed to perform the correlation of k multilevel css when compared to those required with a straightforward architecture furthermore these architectures can be used as a starting point for the search of multilevel css with low peak to average power ratio papr and flexible length

quaternary constant amplitude codes for multicode cdma a constant amplitude code is a code that reduces the peak to average power ratio papr in multicode code division multiple access mc cdma systems to the favorable value 1 in this paper quaternary constant amplitude codes codes over z 4 of length 2 m with error correction capabilities are studied these codes exist for every positive integer m while binary constant amplitude codes cannot exist if m is odd every word of such a code corresponds to a function from the binary m tuples to z4 having the bent property i e its fourier transform has magnitudes 2 m 2 several constructions of such functions are presented which are exploited in connection with algebraic codes over z4 in particular quaternary reed muller kerdock and delsarte goethals codes to construct families of quaternary constant amplitude codes mappings from binary to quaternary constant amplitude codes are presented as well

new 64 qam golay complementary sequences a construction of 64 qam golay complementary sequences was proposed by lee and golomb where three qpsk golay davis jedwab complementary sequences gdj sequences or standard golay sequences related by a pair of offsets were combined to form each 64 qam golay sequence feasible offset pairs were given as first order generalized boolean functions in algebraic normal form new offset pairs were described in a conjecture of li leading to new 64 qam golay complementary sequences the proof of the conjecture is presented

complementary set matrices satisfying a column correlation constraint motivated by the problem of reducing the peak to average power ratio papr of transmitted signals we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint the design algorithm recursively builds a collection of 2t 1 mutually orthogonal mo complementary set matrices starting from a companion pair of sequences we relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate companion pair to ensure that a given column correlation constraint is satisfied for t 0 companion pair properties directly determine matrix column correlation properties the proposed companion pair based design can construct binary complementary sets with either a minimum out of phase autocorrelation magnitude or a minimum sum of out of phase autocorrelation magnitude for column sequences of length at least up to 28 for t ges 1 reducing correlation merits of the companion pair may lead to improved column correlation properties exhaustive search for companion pairs satisfying a column correlation constraint is infeasible for medium length and long sequences we instead search for two shorter length sequences by minimizing a cost function in terms of their autocorrelation and cross correlation merits in addition by exploiting the well known welch bound sufficient conditions for the existence of companion pairs which satisfy a set of column correlation constraints are given

a framework for the construction ofgolay sequences in 1999 davis and jedwab gave an explicit algebraic normal form for m 2 2h m 1 ordered golay pairs of length 2mmiddot over z2h involving m 2 2h m 1 golay sequences in 2005 li and chu unexpectedly found an additional 1024 length 16 quaternary golay sequences fiedler and jedwab showed in 2006 that these new golay sequences exist because of a crossover of the aperiodic autocorrelation function of certain quaternary length eight sequences belonging to golay pairs and that they spawn further new quaternary golay sequences and pairs of length 2m for m 4 under budisin s 1990 iterative construction the total number of golay sequences and pairs spawned in this way is counted and their algebraic normal form is given explicitly a framework of constructions is derived in which turyn s 1974 product construction together with several variations plays a key role all previously known golay sequences and pairs of length 2m over z2h can be obtained directly in explicit algebraic normal form from this framework furthermore additional quaternary golay sequences and pairs of length 2m are produced that cannot be obtained from any other known construction the framework generalizes readily to lengths that are not a power of 2 and to alphabets other than z2h

a new construction of 64 qam golay complementary sequences in this correspondence we present a new construction for 64 qam golay sequences of length n 2 sup m for integer m the peak envelope power pep of 64 qam golay sequences is shown to be bounded by 4 66n the new construction of 64 qam golay sequences of length n 2 sup m is based on our earlier construction of new offsets of 16 qam golay sequences which are also presented here the total number of offsets of 64 qam golay sequences is 496 for m 2 808 for m 3 and 976 for m 4 obtained by computer search we also computed the pep distribution for 64 qam golay sequences for m 2 m 3 and m 4

the derived category of quasi coherent sheaves and axiomatic stable homotopy we prove in this paper that for a quasi compact and semi separated nonnecessarily noetherian scheme x the derived category of quasi coherent sheaves over x is a stable homotopy category in the sense of hovey palmieri and strickland answering a question posed by strickland moreover we show that it is unital and algebraic we also prove that for a noetherian semi separated formal scheme its derived category of sheaves of modules with quasi coherent torsion homologies is a stable homotopy category it is algebraic but if the formal scheme is not a usual scheme it is not unital therefore its abstract nature differs essentially from that of the derived category which is equivalent to in the case of a usual scheme

feedback strategies for discrete time linear quadratic two player descriptor games this paper deals with discrete time linear quadratic descriptor two player games the two frameworks of nash and stackelberg strategies with feedback information structure are considered the aim is to provide sufficient conditions ensuring for any initial state the existence and the uniqueness of a tri trajectory gathering the state and the controls of the two players which reaches the equilibrium the provided results are mainly based on a discrete time matrix block formulation the provided algorithms consist in an iterative backward in time procedure issued from dynamic programming numerical examples illustrate this approach and the particular case of explicit systems is recovered for both kinds of strategies

efficient architectures for the generation and correlation of binary css derived from different kernel lengths complementary sets of sequences css are used as basic building blocks for the development of generalized orthogonal go sequences in the design of practical sequences are desirable both optimal correlation properties and an efficient implementation of their corresponding correlators i e with a reduced number of operations per input sample traditionally the efficient algorithms for the generation correlation of k binary css have been constrained to those of lengths l kn where k 2 and n is a non negative integer this constraint implies that many binary css of known lengths cannot be generated and correlated efficiently thus limiting their practical application this paper proposes novel efficient architectures for the generation and correlation of k binary css of length l k 2 2n 10m 26p with n m and p non negative integers the proposal allows the efficient generation and correlation of binary css of many more lengths than previous efficient architectures can handle therefore the use of the proposed architectures allows selecting with more flexibility the processing gain needed for each particular application

a new construction of 16 qam near complementary sequences we present a new 16 qam near complementary sequence construction where the length of the sequences is n 2m the 16 qam near complementary sequences are constructed by nonlinear offsets but the peak to mean envelope power ratio bounds for these 16 qam near complementary sequences is as low as 2 4 the number of newly constructed 16 qam near complementary sequences is m 2 4m 1

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

homotopical algebraic geometry i topos theory this is the rst of a series of papers devoted to lay the foundations of algebraic geometry in homotopical and higher categorical contexts in this rst part we investigate a notion of higher topos for this we use s categories i e simplicially enriched categories as models for certain kind of 1 categories and we develop the notions of s topologies s sites and stacks over them we prove in particular that for an s category t endowed with an s topology there exists a model category of stacks over t generalizing the model category structure on simplicial presheaves over a grothendieck site of a joyal and r jardine we also prove some analogs of the relations between topologies and localizing subcategories of the categories of presheaves by proving that there exists a one to one correspodence between s topologies on an s category t and certain left exact bouseld localizations of the model category of pre stacks on t based on the above results we study the notion of model topos introduced by c rezk and we relate it to our model categories of stacks over s sites in the second part of the paper we present a parallel theory where s categories s topologies and s sites are replaced by model categories model topologies and model sites we prove that a canonical way to pass from the theory of stacks over model sites to the theory of stacks over s sites is provided by the simplicial localization construction of dwyer and kan as an example of application we propose a denition of etale k theory of ring spectra extending the etale k theory of commutative rings

more golay sequences davis and jedwab s construction of golay sequences as reed muller codewords was believed to generate possibly all golay sequences over z sub 2 sup h of length 2 sup m from exhaustive search 1024 quaternary h 2 golay sequences of length 16 m 4 are found which are not within davis and jedwab s construction a table of 16 characteristic sequences is presented from which all 1024 golay sequences can be reconstructed the pairing information and the papr s of associated ofdm signals are given