Anticanonical codes from del Pezzo surfaces with Picard rank one

Blache, Régis; Couvreur, Alain; Hallouin, Emmanuel; Madore, David; Nardi, Jade; Rambaud, Matthieu; Randriam, Hugues

doi:10.1090/tran/8119

Anticanonical codes from del Pezzo surfaces with Picard rank one
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by Régis Blache, Alain Couvreur, Emmanuel Hallouin, David Madore, Jade Nardi, Matthieu Rambaud and Hugues Randriam PDF

Trans. Amer. Math. Soc. 373 (2020), 5371-5393 Request permission

Abstract:

We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank $1$ 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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