DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Fifty six
TITLE: "Codes and Association Schemes"
EDITORS: Alexander Barg and Simon Litsyn

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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

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Document last modified on September 27, 2001.