DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

### Ordering Information

This volume may be obtained from the AMS or through bookstores in your area.

To order through AMS contact the AMS Customer Services Department, P.O. Box 6248, Providence, Rhode Island 02940-6248 USA. For Visa, Mastercard, Discover, and American Express orders call 1-800-321-4AMS.

You may also visit the AMS Bookstore and order directly from there. DIMACS does not distribute or sell these books.

### PREFACE

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

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



Index of Volumes
DIMACS Homepage
Contacting the Center