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arXiv · 2410.11968

Codes on Weighted Projective Planes

Yağmur Çakıroğlu·Jade Nardi·Mesut Şahin
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Abstract

We comprehensively study weighted projective Reed-Muller (WPRM) codes on weighted projective planes $\mathbb{P}(1,a,b)$. We provide the universal Gr\"obner 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.

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Yağmur Çakıroğlu, Jade Nardi, Mesut Şahin. 2024-10-15. Codes on Weighted Projective Planes. https://arxiv.org/abs/2410.11968

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