Codes and Association Schemes: DIMACS Workshop Codes and Association Schemes, November 9-12, 1999, DIMACS Center

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Alexander Barg, Simon Litsyn
American Mathematical Soc., Jan 1, 2001 - Mathematics - 303 pages
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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.

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Numerical results on the asymptotic rate of binary codes
Indexes of spherical codes
Bent resilient functions and the Numerical Normal Form
Ternary Hamming and binary perfect covering codes
On perfect codes in the Johnson scheme
Integral zeroes of Krawtchouk polynomials
Some algebra related to P and Qpolynomial association schemes
Bounds for the ChristoffelDarboux kernel of the binary Krawtchouk
On an algebraic method for bounding the covering radius
The isomorphism problem for circulant graphs via Schur ring theory
New generator quasitwisted codes over GF5
Estimates of the distance distribution of nonbinary codes with applications

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