Codes from $A_m$-invariant polynomials
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929633530740736 |
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| author | Micheli, Giacomo Lavorante, Vincenzo Pallozzi Waitkevich, Phillip |
| author_facet | Micheli, Giacomo Lavorante, Vincenzo Pallozzi Waitkevich, Phillip |
| contents | Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with Generalized Reed-Muller codes with similar parameters, our codes have the same asymptotic relative distance but a better rate. Our results follow from combinations of Galois theoretical methods with Weil-type bounds for the number of points of hypersurfaces over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codes from $A_m$-invariant polynomials Micheli, Giacomo Lavorante, Vincenzo Pallozzi Waitkevich, Phillip Information Theory Number Theory Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with Generalized Reed-Muller codes with similar parameters, our codes have the same asymptotic relative distance but a better rate. Our results follow from combinations of Galois theoretical methods with Weil-type bounds for the number of points of hypersurfaces over finite fields. |
| title | Codes from $A_m$-invariant polynomials |
| topic | Information Theory Number Theory |
| url | https://arxiv.org/abs/2412.12005 |