Codes on Weighted Projective Planes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916776451768320 |
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| author | Çakıroğlu, Yağmur Nardi, Jade Şahin, Mesut |
| author_facet | Çakıroğlu, Yağmur Nardi, Jade Şahin, Mesut |
| contents | We comprehensively study weighted projective Reed-Muller (WPRM) codes on weighted projective planes $\mathbb{P}(1,a,b)$. We provide the universal Gröbner basis for the vanishing ideal of the set $Y$ of $\mathbb{F}_q$--rational points of $\mathbb{P}(1,a,b)$ to get the dimension of the code. We determine the regularity set of $Y$ using a novel combinatorial approach. We employ footprint techniques to compute the minimum distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codes on Weighted Projective Planes Çakıroğlu, Yağmur Nardi, Jade Şahin, Mesut Algebraic Geometry Information Theory We comprehensively study weighted projective Reed-Muller (WPRM) codes on weighted projective planes $\mathbb{P}(1,a,b)$. We provide the universal Gröbner basis for the vanishing ideal of the set $Y$ of $\mathbb{F}_q$--rational points of $\mathbb{P}(1,a,b)$ to get the dimension of the code. We determine the regularity set of $Y$ using a novel combinatorial approach. We employ footprint techniques to compute the minimum distance. |
| title | Codes on Weighted Projective Planes |
| topic | Algebraic Geometry Information Theory |
| url | https://arxiv.org/abs/2410.11968 |