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Anticanonical codes from del Pezzo surfaces with Picard rank one

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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https://hal.archives-ouvertes.fr/hal-02075926
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Submitted on : Thursday, March 21, 2019 - 5:15:42 PM
Last modification on : Monday, November 22, 2021 - 12:34:02 PM
Long-term archiving on: : Saturday, June 22, 2019 - 3:51:07 PM

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Régis Blache, Alain Couvreur, Emmanuel Hallouin, David Madore, Jade Nardi, et al.. Anticanonical codes from del Pezzo surfaces with Picard rank one. Transactions of the American Mathematical Society, American Mathematical Society, 2020, ⟨10.1090/tran/8119⟩. ⟨hal-02075926⟩

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