Hulls of Projective Reed-Muller Codes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914829456900096 |
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| author | Kaplan, Nathan Kim, Jon-Lark |
| author_facet | Kaplan, Nathan Kim, Jon-Lark |
| contents | Projective Reed-Muller codes are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. We consider the relationship between projective Reed-Muller codes and their duals. We determine when these codes are self-dual, when they are self-orthogonal, and when they are LCD. We then show that when $q$ is sufficiently large, the dimension of the hull of a projective Reed-Muller code is 1 less than the dimension of the code. We determine the dimension of the hull for a wider range of parameters and describe how this leads to a new proof of a recent result of Ruano and San José (2024). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hulls of Projective Reed-Muller Codes Kaplan, Nathan Kim, Jon-Lark Information Theory Discrete Mathematics 11T71, 94B60, 11T06 Projective Reed-Muller codes are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. We consider the relationship between projective Reed-Muller codes and their duals. We determine when these codes are self-dual, when they are self-orthogonal, and when they are LCD. We then show that when $q$ is sufficiently large, the dimension of the hull of a projective Reed-Muller code is 1 less than the dimension of the code. We determine the dimension of the hull for a wider range of parameters and describe how this leads to a new proof of a recent result of Ruano and San José (2024). |
| title | Hulls of Projective Reed-Muller Codes |
| topic | Information Theory Discrete Mathematics 11T71, 94B60, 11T06 |
| url | https://arxiv.org/abs/2406.04757 |