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This volume presents papers related to the DIMACS workshop, "Codes and Association Schemes" held in November 1999. 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 C. Bachoc Numerical results on the asymptotic rate of binary codes A. Barg and D. B. Jaffe 25 Weakly biased arrays, almost independent arrays and error-correcting codes J. Bierbrauer and H. Schellwat 33 Indexes of spherical codes P. Boyvalenkov, D. Danev, and P. Kazakov 47 Codes over Zpn and association schemes P. Camion 59 Bent, resilient functions and the numerical normal form C. Carlet and P. Guillot 87 On identifying codes G. D. Cohen, I. Honkala, A. Lobstein, and G. Zémor 97 Ternary Hamming and binary perfect covering codes I. J. Dejter and K. T. Phelps 111 A Riemann hypothesis analogue for self-dual codes I. Duursma 115 On perfect codes in the Johnson scheme T. Etzion 125 On perfect constant weight codes T. Etzion and J. van Lint 131 On additive GF(4) codes P. Gaborit, W. C. Huffman, J.-L. Kim, and V. Pless 135 Integral zeroes of Krawtchouk polynomials L. Habsieger 151 Some algebra related to P- and Q-polynomial association schemes T. Ito, K. Tanabe, and P. Terwilliger 167 Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials I. Krasikov 193 Survey of binary Krawtchouk polynomials I. Krasikov and S. Litsyn 199 On an algebraic method for bounding the covering radius T. Laihonen 213 Design systems: Combinatorial characterizations of Delsarte $\mathcal T$-designs via partially ordered sets W. J. Martin 223 The isomorphism problem for circulant graphs via Schur ring theory M. Muzychuk, M. Klin, and R. Pöschel 241 New 1-generator quasi-twisted codes over GF(5) I. Siap, N. Aydin, and D. Ray-Chaudhuri 265 Communication complexity and orthogonal polynomials U. Tamm 277 Estimates of the distance distribution of nonbinary codes, with applications A. Ashikhmin, A. Barg, and S. Litsyn 287