An Algorithm for Computing the Covering Radius of a Linear Code Based on Vilenkin-Chrestenson Transform
Information Theory
2022-02-25 v1 Discrete Mathematics
Combinatorics
math.IT
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.
Keywords
Cite
@article{arxiv.2202.12111,
title = {An Algorithm for Computing the Covering Radius of a Linear Code Based on Vilenkin-Chrestenson Transform},
author = {Paskal Piperkov and Iliya Bouyukliev and Stefka Bouyuklieva},
journal= {arXiv preprint arXiv:2202.12111},
year = {2022}
}