Codes and Association Schemes

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More About This Textbook

Overview

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.

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Editorial Reviews

Booknews
Contains papers from a November 1999 workshop held to demonstrate new applications of the theory of association schemes to coding and to give coding theorists an opportunity to familiarize themselves with new properties of association schemes, both polynomial and general. Themes include applications of association schemes to codes, applications of the polynomial method, structural results for codes, structural results for schemes, and properties of orthogonal polynomials and their applications in combinatorics. Specific topics include indexes of spherical codes, a Riemann hypothesis analogue for self-dual codes, numerical results on the asymptotic rate of binary codes, and integral zeroes of Krawtchouk polynomials. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821820742
  • Publisher: American Mathematical Society
  • Publication date: 2/13/2001
  • Series: DIMACS Series , #56
  • Pages: 303
  • Product dimensions: 6.30 (w) x 9.06 (h) x 0.87 (d)

Table of Contents

Preface
Foreword
Harmonic weight enumerators of nonbinary codes and MacWilliams identities 1
Numerical results on the asymptotic rate of binary codes 25
Weakly biased arrays, almost independent arrays and error-correcting codes 33
Indexes of spherical codes 47
Codes over Z[subscript p[superscript n]] and association schemes 59
Bent, resilient functions and the Numerical Normal Form 87
On identifying codes 97
Ternary Hamming and binary perfect covering codes 111
A Riemann hypothesis analogue for self-dual codes 115
On perfect codes in the Johnson scheme 125
On perfect constant weight codes 131
On additive GF(4) codes 135
Integral zeroes of Krawtchouk polynomials 151
Some algebra related to P- and Q-polynomial association schemes 167
Bounds for the Christoffel-Darboux kernel of the binary Krawtchouk polynomials 193
Survey of binary Krawtchouk polynomials 199
On an algebraic method for bounding the covering radius 213
Design systems: Combinatorial characterizations of Delsarte T-designs via partially ordered sets 223
The isomorphism problem for circulant graphs via Schur ring theory 241
New 1-generator quasi-twisted codes over GF(5) 265
Communication complexity and orthogonal polynomials 277
Estimates of the distance distribution of nonbinary codes, with applications 287
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