New advances in permutation decoding of first-order Reed-Muller codes

In this paper we describe a variation of the classical permu-tation 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 algorithm we improve considerably the num-ber of errors we can correct in comparison with the known results in this topic.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

Automated summary

In this paper, a modified permutation decoding algorithm is proposed for affine-invariant codes with respect to certain type of information sets. The algorithm is applied to the first-order Reed-Muller codes with the information sets introduced in [2], significantly improving the error correction capability compared to existing results in this field.