An Algorithm for Computing the Covering Radius of a Linear Code Based on Vilenkin-Chrestenson Transform

TL;DR

This paper introduces a modified Vilenkin-Chrestenson transform tailored for efficient computation of the covering radius and weight distribution of linear codes over finite fields, reducing complexity compared to traditional methods.

Contribution

It proposes a novel transform based on a subset of vectors, enabling faster calculations of code parameters in coding theory.

Findings

Reduced computational complexity for covering radius calculation

Effective generalization of Vilenkin-Chrestenson transform

Potential for improved coding theory applications

Abstract

We present a generalization of Walsh-Hadamard transform that is suitable for applications in Coding Theory, especially for computation of the weight distribution and the covering radius of a linear code over a finite field. The transform used in our research, is a modification of Vilenkin-Chrestenson transform. Instead of using all the vectors in the considered space, we take a maximal set of nonproportional vectors, which reduces the computational complexity.