Construction of good codes from weak Del Pezzo surfaces

2023/01/27 by Régis Blache, Blache, Régis, Emmanuel Hallouin +1 · 1 citation
Computer Science · Mathematics · Medicine · #14G50 #14J26 #94B27 #Algebraic Geometry (math.AG) #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2301.11825

openalex publication_date 2023/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct algebraic geometric codes from weak del Pezzo surfaces. The codes are associated to the anti-canonical class of the anti-canonical model and to the set of rational points of these models. Since we consider weak Del Pezzo surfaces, the anti canonical model is not smooth any more. This complicates the computation of the parameters of the codes; in particular we need to distinguish the Cartier divisors from the Weil ones.

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