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Codes and Association Schemes: DIMACS Workshop Codes and Association Schemes, November 9-12, 1999, DIMACS Center [Kietas viršelis]

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This volume presents papers related to the DIMACS workshop, ""Codes and Association Schemes"". The articles are devoted to the following topics: applications of association schemes and of the polynomial method to properties of codes, structural results for codes, structural results for association schemes, and properties of orthogonal polynomials and their applications in combinatorics. Papers on coding theory are related to classical topics, such as perfect codes, bounds on codes, codes and combinatorial arrays, weight enumerators, and spherical designs. Papers on orthogonal polynomials provide new results on zeros and symptotic properties of standard families of polynomials encountered in coding theory. The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. It offers a solid representation of results in problems in areas of current interest.
Preface ix Foreword xi Harmonic weight enumerators of nonbinary codes and MacWilliams identities 1(24) Christine Bachoc Numerical results on the asymptotic rate of binary codes 25(8) Alexander Barg David B. Jaffe Weakly biased arrays, almost independent arrays and error-correcting codes 33(14) Jurgen Bierbrauer Holger Schellwat Indexes of spherical codes 47(12) Peter Boyvalenkov Danyo Danev Peter Kazakov Codes over Zpn and association schemes 59(28) Paul Camion Bent, resilient functions and the Numerical Normal Form 87(10) Claude Carlet Philippe Guillot On identifying codes 97(14) Gerard D. Cohen Iiro Honkala Antoine Lobstein Gilles Zemor Ternary Hamming and binary perfect covering codes 111(4) Italo J. Dejter Kevin T. Phelps A Riemann hypothesis analogue for self-dual codes 115(10) Iwan Duursma On perfect codes in the Johnson scheme 125(6) Tuvi Etzion On perfect constant weight codes 131(4) Tuvi Etzion Jack van Lint On additive GF(4) codes 135(16) Philippe Gaborit W. Cary Huffman Jon-Lark Kim Vera Pless Integral zeroes of Krawtchouk polynomials 151(16) Laurent Habsieger Some algebra related to P- and Q-polynomial association schemes 167(26) Tatsuro Ito Kenichiro Tanabe Paul Terwilliger Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials 193(6) Ilia Krasikov Survey of binary Krawtchouk polynomials 199(14) Ilia Krasikov Simon Litsyn On an algebraic method for bounding the covering radius 213(10) Tero Laihonen Design systems: Combinatorial characterizations of Delsarte T-designs via partially ordered sets 223(18) William J. Martin The isomorphism problem for circulant graphs via Schur ring theory 241(24) Mikhail Muzychuk Mikhail Klin Reinhard Poschel New 1-generator quasi-twisted codes over GF(5) 265(12) Irfan Siap Nuh Aydin Dijen Ray-Chaudhuri Communication complexity and orthogonal polynomials 277(10) Ulrich Tamm Estimates of the distance distribution of nonbinary codes, with applications 287 Alexei Ashikhmin Alexander Barg Simon Litsyn