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Codes and Association Schemes
Edited by: Alexander Barg, Bell Labs - Lucent Technologies, Murray Hill, NJ, and Simon Litsyn, Tel Aviv University, Israel
A co-publication of the AMS and DIMACS.
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DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
2001; 303 pp; hardcover
Volume: 56
ISBN-10: 0-8218-2074-5
ISBN-13: 978-0-8218-2074-2
List Price: US$103
Member Price: US$82.40
Order Code: DIMACS/56
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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.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).

Readership

Graduate students and research mathematicians interested in coding theory, algebraic combinatorics, and computer science.

Table of Contents

  • C. Bachoc -- Harmonic weight enumerators of nonbinary codes and MacWilliams identities
  • A. Barg and D. B. Jaffe -- Numerical results on the asymptotic rate of binary codes
  • J. Bierbrauer and H. Schellwat -- Weakly biased arrays, almost independent arrays and error-correcting codes
  • P. Boyvalenkov, D. Danev, and P. Kazakov -- Indexes of spherical codes
  • P. Camion -- Codes over \(\mathbb Z_{p^n}\) and association schemes
  • C. Carlet and P. Guillot -- Bent, resilient functions and the numerical normal form
  • G. D. Cohen, I. Honkala, A. Lobstein, and G. Zémor -- On identifying codes
  • I. J. Dejter and K. T. Phelps -- Ternary Hamming and binary perfect covering codes
  • I. Duursma -- A Riemann hypothesis analogue for self-dual codes
  • T. Etzion -- On perfect codes in the Johnson scheme
  • T. Etzion and J. van Lint -- On perfect constant weight codes
  • P. Gaborit, W. C. Huffman, J.-L. Kim, and V. Pless -- On additive \(GF(4)\) codes
  • L. Habsieger -- Integral zeroes of Krawtchouk polynomials
  • T. Ito, K. Tanabe, and P. Terwilliger -- Some algebra related to \(P\)- and \(Q\)-polynomial association schemes
  • I. Krasikov -- Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials
  • I. Krasikov and S. Litsyn -- Survey of binary Krawtchouk polynomials
  • T. Laihonen -- On an algebraic method for bounding the covering radius
  • W. J. Martin -- Design systems: Combinatorial characterizations of Delsarte \(\mathcal T\)-designs via partially ordered sets
  • M. Muzychuk, M. Klin, and R. Pöschel -- The isomorphism problem for circulant graphs via Schur ring theory
  • I. Siap, N. Aydin, and D. Ray-Chaudhuri -- New 1-generator quasi-twisted codes over GF(5)
  • U. Tamm -- Communication complexity and orthogonal polynomials
  • A. Ashikhmin, A. Barg, and S. Litsyn -- Estimates of the distance distribution of nonbinary codes, with applications
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