spherical codes generated by binary partitions of symmetric pointsets several constructions are presented by which spherical codes are generated from groups of binary codes in the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line the main ideas are code concatenation and set partitioning extensive tables are presented for spherical codes in dimension n spl les 24

a construction for constant composition codes by employing the residue polynomials we give a construction of constant composition codes this construction generalizes the one proposed by xing 2002 it turns out that when d 3 this construction gives a lower bound of constant composition codes improving the one by luo 2003 for some case moreover for d 3 we give a lower bound on maximal size of constant composition codes in particular our bound for d 5 gives the best possible size of constant composition codes up to magnitude

linear size optimal q ary constant weight codes and constant composition codes an optimal constant composition or constant weight code of weight w has linear size if and only if its distance d is at least 2w 1 when d 2w the determination of the exact size of such a constant composition or constant weight code is trivial but the case of d 2w 1 has been solved previously only for binary and ternary constant composition and constant weight codes and for some sporadic instances this paper provides a construction for quasicyclic optimal constant composition and constant weight codes of weight w and distance 2w 1 based on a new generalization of difference triangle sets as a result the sizes of optimal constant composition codes and optimal constant weight codes of weight w and distance 2w 1 are determined for all such codes of sufficiently large lengths this solves an open problem of etzion the sizes of optimal constant composition codes of weight w and distance 2w 1 are also determined for all w 6 except in two cases

permutation codes for the gaussian channel the initial vector problem is considered for group codes for the gaussian channel and in particular for codes generated by permutation groups variant i and variant ii permutation codes are defined and optimal initial vectors for these codes are constructed a numerical algorithm for constructing optimal group codes is presented together with examples of this algorithm applied to several permutation groups

quaternary constant composition codes with weight 4 and distances 5 or 6 the sizes of optimal constant composition codes cccs of weight 3 have been determined by chee ge and ling with four cases in doubt group divisible codes gdcs played an important role in their constructions in this paper we study the problem of constructing optimal quaternary cccs with hamming weight 4 and minimum distances 5 or 6 through gdcs and room square approaches the problem is solved leaving only five lengths undetermined previously the results on the sizes of such quaternary cccs were scarce

bounds for codes over the unit circle let c be a code of length n and rate r over the alphabet a q exp 2 pi ir q r o 1 cdots q 1 and let d c be the minimum euclidean distance of c for large n the lower and upper bounds are obtained in parametric form on the achievable pairs r delta where delta d 2 c n holds to obtain these bounds the arguments leading to the gilbert bound and the elias bound respectively are applied to the alphabet a q for q rightarrow infty they are shown to be expressible in terms of the modified bessel function of the first kind the elias type bound is compared with the kabatyanskii levenshtein k l bound that holds for less restrictive alphabets it turns out that our upper bound improves the k l bound for delta leq 0 93

tables of sphere packings and spherical codes the theta function of a sphere packing gives the number of centers at each distance from the origin the theta functions of a number of important packings a n d n e n the leech lattice and others and tables of the first fifty or so of their coefficients are given in this paper

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

superconvergent functional output for time dependent problems using finite differences on summation by parts form finite difference operators satisfying the summation by parts sbp rules can be used to obtain high order accurate energy stable schemes for time dependent partial differential equations when the boundary conditions are imposed weakly by the simultaneous approximation term sat in general an sbp sat discretization is accurate of order p 1 with an internal accuracy of 2p and a boundary accuracy of p despite this it is shown in this paper that any linear functional computed from the time dependent solution will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way the method does not involve the solution of the dual equations and superconvergent functionals are obtained at no extra computational cost four representative model problems are analyzed in terms of convergence and errors and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs

deformation obstruction theory for complexes via atiyah and kodaira spencer classes we give a universal approach to the deformation obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family we recover and generalise the obstruction class of lowen and lieblich and prove that it is a product of atiyah and kodaira spencer classes this allows us to obtain deformation invariant virtual cycles on moduli spaces of objects of the derived category on threefolds

a well balanced and entropy conservative discontinuous galerkin spectral element method for the shallow water equations in this work we design an arbitrary high order accurate nodal discontinuous galerkin spectral element type method for the one dimensional shallow water equations the novel method uses a skew symmetric formulation of the continuous problem we prove that this discretisation exactly preserves the local mass and momentum furthermore we show that combined with a special numerical interface flux function the method exactly preserves the entropy which is also the total energy for the shallow water equations finally we prove that the surface fluxes the skew symmetric volume integrals and the source term are well balanced numerical tests are performed to demonstrate the theoretical findings

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

a new construction of zero difference balanced functions and its applications in this paper a new construction of zero difference balanced functions defined on is given where is an odd positive integer based on the generic constructions proposed by ding optimal constant composition codes and perfect difference systems of sets with new parameters can be generated from the zero difference balanced functions constructed in this paper

some new classes of zero difference balanced functions zero difference balanced zdb functions were introduced recently by ding for the construction of optimal constant composition codes and optimal and perfect difference systems of sets they are closely related to partitioned difference families in this paper we present generic constructions of zdb functions from functions with difference balanced property in particular two classes of zdb functions with new and flexible parameters are reported employing these new zdb functions we obtain at the same time optimal 1 constant composition codes 2 constant weight codes and 3 perfect difference systems of sets all with new and flexible parameters

group divisible codes and their application in the construction of optimal constant composition codes of weight three the concept of group divisible codes a generalization of group divisible designs with constant block size is introduced in this paper this new class of codes is shown to be useful in recursive constructions for constant weight and constant composition codes large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant composition codes of weight three and specified distance leaving only four cases undetermined previously the sizes of constant composition codes of weight three were known only for those of sufficiently large length

constructions of ternary constant composition codes with weight three we consider the problem of determining the maximum size of a ternary code with constant composition and hamming weight three we give several constructions of codes having maximum size and we also present an improvement of the johnson 1962 bound the results presented solve the problem for all lengths when d 3 as well as for lengths 7 11 and all even lengths when d 4

upper bounds for constant weight codes let a n d w denote the maximum possible number of codewords in an n d w constant weight binary code we improve upon the best known upper bounds on a n d w in numerous instances for n spl les 24 and d spl les 12 which is the parameter range of existing tables most improvements occur for d 8 10 where we reduce the upper bounds in more than half of the unresolved cases we also extend the existing tables up to n spl les 28 and d spl les 14 to obtain these results we develop new techniques and introduce new classes of codes we derive a number of general bounds on a n d w by means of mapping constant weight codes into euclidean space this approach produces among other results a bound on a n d w that is tighter than the johnson bound a similar improvement over the best known bounds for doubly constant weight codes studied by johnson and levenshtein is obtained in the same way furthermore we introduce the concept of doubly bounded weight codes which may be thought of as a generalization of the doubly constant weight codes subsequently a class of euclidean space codes called zonal codes is introduced and a bound on the size of such codes is established this is used to derive bounds for doubly bounded weight codes which are in turn used to derive bounds on a n d w we also develop a universal method to establish constraints that augment the delsarte inequalities for constant weight codes used in the linear programming bound in addition we present a detailed survey of known upper bounds for constant weight codes and sharpen these bounds in several cases all these bounds along with all known dependencies among them are then combined in a coherent framework that is amenable to analysis by computer this improves the bounds on a n d w even further for a large number of instances of n d and w

on constant composition codes over z sub q a constant composition code is a special constant weight code under the restriction that each symbol should appear a given number of times in each codeword in this correspondence we give a lower bound for the maximum size of the q ary constant composition codes with minimum distance at least 3 this bound is asymptotically optimal and generalizes the graham sloane bound for binary constant weight codes in addition three construction methods of constant composition codes are presented and a number of optimum constant composition codes are obtained by using these constructions

summation by parts projections and stability ii we have derived stability results for high order finite difference approximations of mixed hyperbolic parabolic initial boundary value problems ibvp the results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection by slightly rearranging the analytic equations we can prove strict stability for hyperbolic parabolic ibvp furthermore we generalize our technique so as to yield strict stability on curvilinear non smooth domains in two space dimensions finally we show how to incorporate inhomogeneous boundary data while retaining strict stability using the same procedure one can prove strict stability in higher dimensions as well

upper bounds on the minimum distance of spherical codes we use linear programming techniques to obtain new upper bounds on the maximal squared minimum distance of spherical codes with fixed cardinality functions q sub j n s are introduced with the property that q sub j n s m if and only if the levenshtein bound l sub m n s on a n s max w w is an n w s code can be improved by a polynomial of degree at least m 1 general conditions on the existence of new bounds are presented we prove that for fixed dimension n spl ges 5 there exists a constant k k n such that all levenshtein bounds l sub m n s for m spl ges 2k 1 can be improved an algorithm for obtaining new bounds is proposed and discussed

the closest packing of equal circles on a sphere the closest packing of x circles on the surface of a sphere is examined with the use of techniques that have been developed to determine the stereochemical arrangement of atoms packed around a central atom the technique is based on the concept that the centres of the circles repel one another and minimizing the total repulsion energy leads to an approximate structure from which exact solutions can be determined a number of improved packings have been discovered for values of x in the range 20 40 many different types of structure are found that are of lower symmetries than those previously described the packing density p defined as the fraction of the spherical surface that is enclosed by the circles is found to increase as the number of circles increases in contrast to the conclusion from previous studies however this increase in p is very slight and the values remain substantially below that for an infinite number of circles or a close packed plane

cyclotomic constructions of zero difference balanced functions with applications based on a recent work of ding wang and xiong we present some cyclotomic constructions of zero difference balanced zdb functions which interpret the previous construction proposed by cai zeng helleseth tang and yang the resulted zdb functions can be used to generate optimal constant composition codes and perfect difference systems of sets with new parameters

stable and accurate wave propagation in discontinuous media a time stable discretization is derived for the second order wave equation with discontinuous coefficients the discontinuity corresponds to inhomogeneity in the underlying medium and is treated by splitting the domain each homogeneous sub domain is discretized using narrow diagonal summation by parts operators and then patched to its neighbors by using a penalty method leading to fully explicit time integration this discretization yields a time stable and efficient scheme the analysis is verified by numerical simulations in one dimension using high order finite difference discretizations and in three dimensions using an unstructured finite volume discretization

optimized permutation modulation permutation modulation is a class of group codes for the gaussian channel a group code is a set of vectors obtained by a group of orthogonal matrices operating on an initial vector an important problem is to find the initial vector yielding the largest minimum euclidean distance between two vectors this problem is solved for permutation modulation the performance of such optimized permutation modulation is analyzed compared to binary antipodal signals and psk phase shift keying it typically requires 2 5 4 db less energy for the same minimum distance

the pbd closure of constant composition codes we show an interesting pairwise balanced design pbd closure result for the set of lengths of constant composition codes whose distance and size meet certain conditions a consequence of this pbd closure result is that the size of optimal constant composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code as an application the sizes of several infinite families of optimal constant composition codes are derived in particular the problem of determining the size of optimal constant composition codes having distance four and weight three is solved for all lengths sufficiently large this problem was previously unresolved for odd lengths except for lengths seven and eleven

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

asymptotically dense spherical codes i wrapped spherical codes a new class of spherical codes called wrapped spherical codes is constructed by wrapping any sphere packing spl lambda in euclidean space onto a finite subset of the unit sphere in one higher dimension the mapping preserves much of the structure of spl lambda and unlike previously proposed maps the density of the wrapped spherical codes approaches the density of spl lambda as the minimum distance approaches zero we show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever spl lambda is the densest possible sphere packing