English

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.

Keywords

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}
}
R2 v1 2026-06-28T08:36:56.458Z