Codes and Association Schemes

Codes and Association Schemes

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This volume presents papers related to the DIMACS workshop, qCodes and Association Schemesq. 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.In an arbitrary connected graph G, an r-identifying code C is called perfect, if Br(v) nC has cardinality one, if v is a codeword, and cardinality ... If C is a perfect r- identifying code in G, then for all distinct codewords c, ca#39; e C. we have d(c, ca#39;) agt; 2r.

Title:Codes and Association Schemes
Author:Alexander Barg, Simon Litsyn
Publisher:American Mathematical Soc. - 2001-01-01


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