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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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