Polynomial method in coding and information theory

Details Polynomial method in coding and information theory Polynomial method in coding and information theory

Publishing date

1999-10-31

URL

arxiv.org/abs/math/9910175v1

Science

Mathematics

Field

Combinatorics

Additional info

11 pages

Type

Scientific paper

Abstract

Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the applicability of the method was extended to cover a wider range of problems in coding and information theory. In this paper we present a general framework for the method which includes previous results as particular cases. We explain how this generalization leads to new asymptotic bounds on the performance of codes in binary-input memoryless channels and the Gaussian channel, which improve the results of Shannon et al. of 1959-67, and to a number of other results in combinatorial coding theory.

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