This article is cited in 9 papers

Coding Theory

Spectral Approach to Linear Programming Bounds on Codes

A. M. Barg^ab, D. Yu. Nogin<sup>a

a</sup> Institute for Information Transmission Problems, Russian Academy of Sciences
^b University of Maryland

Abstract: We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte?s linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal polynomials. Examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in projective spaces.

UDC: 621.391.15:681

Received: 09.12.2005
Revised: 01.03.2006

 English version: Problems of Information Transmission, 2006, 42:2, 77–89

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