Spectral approach to linear programming bounds on codes
Alexander Barg, Dmitry Nogin
TL;DR
This paper presents new proofs for asymptotic upper bounds in coding theory using spectral analysis of operators linked to orthogonal polynomials, applicable to various code types.
Contribution
It introduces a spectral approach to linear programming bounds, providing alternative proofs for key asymptotic bounds in coding theory.
Findings
New spectral proofs of asymptotic bounds
Applicable to binary, constant-weight, spherical, and projective codes
Enhances understanding of eigenvector analysis in coding bounds
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. The examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in the projective spaces.
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