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Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics

  • Eiichi Bannai
Part of the NATO ASI Series book series (ASIC, volume 294)

Abstract

This paper surveys the role of orthogonal polynomials in Algebraic Combinatorics, an area which includes association schemes, coding theory, design theory, various theories of group representation, and so on. The main topics discussed in this paper include the following: The connection between orthogonal polynomials and P -polynomial (or Q -polynomial) association schemes. The classification problem for P - and Q -polynomial association schemes and its connection with Askey-Wilson orthogonal polynomials. Delsarte theory of codes and designs in association schemes. The nonexistence of perfect e-codes and tight t-designs through the study of the zeros of orthogonal polynomials. The possible importance of multi-variable versions of Askey-Wilson polynomials in the future study of general commutative association schemes.

Keywords

Orthogonal Polynomial Association Scheme Character Table Perfect Code Primitive Idempotent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Eiichi Bannai
    • 1
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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