New advances in permutation decoding of first-order Reed-Muller codes
Jos\'e Joaqu\'in Bernal, Juan Jacobo Sim\'on
TL;DR
This paper introduces a modified permutation decoding algorithm applicable to affine-invariant codes, notably enhancing error correction capabilities for first-order Reed-Muller codes.
Contribution
It presents a new variation of permutation decoding that improves error correction for first-order Reed-Muller codes using specific information sets.
Findings
Significantly increased error correction compared to previous methods
Applicable to affine-invariant codes beyond Reed-Muller codes
Demonstrated effectiveness on first-order Reed-Muller codes
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.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications