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arXiv · 2302.05189

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

José Joaquín Bernal·Juan Jacobo Simón
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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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José Joaquín Bernal, Juan Jacobo Simón. 2023-02-10. New advances in permutation decoding of first-order Reed-Muller codes. https://arxiv.org/abs/2302.05189

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