Permutation decoding of first-order Generalized Reed-Muller codes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908539408089088 |
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| author | Bernal, José Joaquín Simón, Juan Jacobo |
| author_facet | Bernal, José Joaquín Simón, Juan Jacobo |
| contents | In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study how to implement it for the family of first-order Generalized Reed-Muller codes. Then, we give examples which show that we improve the number of errors we can correct in comparison with the known results for this family of codes. Finally, we deal, from a probabilistic point of view, with the problem of determining when the algorithm only needs to use a smaller PD-like set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutation decoding of first-order Generalized Reed-Muller codes Bernal, José Joaquín Simón, Juan Jacobo Information Theory In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study how to implement it for the family of first-order Generalized Reed-Muller codes. Then, we give examples which show that we improve the number of errors we can correct in comparison with the known results for this family of codes. Finally, we deal, from a probabilistic point of view, with the problem of determining when the algorithm only needs to use a smaller PD-like set. |
| title | Permutation decoding of first-order Generalized Reed-Muller codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.11757 |