Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908849789730816 |
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| author | Lichtenwalner, Monica López, Hiram H. Matthews, Gretchen L. Seneviratne, Padmapani |
| author_facet | Lichtenwalner, Monica López, Hiram H. Matthews, Gretchen L. Seneviratne, Padmapani |
| contents | Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphisms, called a PD set, moves errors out of the information positions so that the original message can be determined. In this paper, we investigate permutation decoding for certain families of algebraic geometry codes. Automorphisms of the underlying curve are used to specify permutation automorphisms of the code. Specifically, we describe permutation decoding sets that correct specific burst errors for one-point codes on Hermitian and norm-trace curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20455 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves Lichtenwalner, Monica López, Hiram H. Matthews, Gretchen L. Seneviratne, Padmapani Information Theory Commutative Algebra 94B05, 11T71, 14G50 Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphisms, called a PD set, moves errors out of the information positions so that the original message can be determined. In this paper, we investigate permutation decoding for certain families of algebraic geometry codes. Automorphisms of the underlying curve are used to specify permutation automorphisms of the code. Specifically, we describe permutation decoding sets that correct specific burst errors for one-point codes on Hermitian and norm-trace curves. |
| title | Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves |
| topic | Information Theory Commutative Algebra 94B05, 11T71, 14G50 |
| url | https://arxiv.org/abs/2602.20455 |