New advances in permutation decoding of first-order Reed-Muller codes
Information Theory
2023-02-13 v1 math.IT
Abstract
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of first-order Reed-Muller codes with respect to the information sets introduced in [2]. Using this algortihm we improve considerably the number of errors we can correct in comparison with the known results in this topic.
Cite
@article{arxiv.2302.05189,
title = {New advances in permutation decoding of first-order Reed-Muller codes},
author = {José Joaquín Bernal and Juan Jacobo Simón},
journal= {arXiv preprint arXiv:2302.05189},
year = {2023}
}