Hull's Parameters of Projective Reed-Muller Code
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917799831535616 |
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| author | Song, Yufeng Luo, Jinquan |
| author_facet | Song, Yufeng Luo, Jinquan |
| contents | Projective Reed-Muller codes(PRM codes) are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. In this paper, we completely determine the minimal distance of the hull of any Projective Reed-Muller codes. Motivated by Nathan Kaplan and Jon-Lark Kim \cite{kaplankim},we extend their results and calculate the hulls' dimension of Projective Reed-Muller Codes in a larger range. We also analyse two special classes of PRM codes apart from self-dual,self-orthgonal and LCD cases, which Kaplan and Kim \cite[section 3]{kaplankim} didn't consider. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07217 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hull's Parameters of Projective Reed-Muller Code Song, Yufeng Luo, Jinquan Information Theory 11T71, 94B60, 11T06 Projective Reed-Muller codes(PRM codes) are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. In this paper, we completely determine the minimal distance of the hull of any Projective Reed-Muller codes. Motivated by Nathan Kaplan and Jon-Lark Kim \cite{kaplankim},we extend their results and calculate the hulls' dimension of Projective Reed-Muller Codes in a larger range. We also analyse two special classes of PRM codes apart from self-dual,self-orthgonal and LCD cases, which Kaplan and Kim \cite[section 3]{kaplankim} didn't consider. |
| title | Hull's Parameters of Projective Reed-Muller Code |
| topic | Information Theory 11T71, 94B60, 11T06 |
| url | https://arxiv.org/abs/2410.07217 |