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arXiv · 1903.09397

Anticanonical codes from del Pezzo surfaces with Picard rank one

Régis Blache·Alain Couvreur·Emmanuel Hallouin·David Madore·Jade Nardi·Matthieu Rambaud·Hugues Randriam
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Abstract

We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit constructions of del Pezzo surfaces of degree 4, 5 and 6, compute the parameters of the associated anticanonical codes and study their isomorphisms arising from the automorphisms of the surface. We obtain codes with excellent parameters and some of them turn out to beat the best known codes listed on the database codetable.

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Régis Blache, Alain Couvreur, Emmanuel Hallouin, David Madore, Jade Nardi, Matthieu Rambaud, Hugues Randriam. 2019-03-22. Anticanonical codes from del Pezzo surfaces with Picard rank one. https://arxiv.org/abs/1903.09397

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