Anticanonical codes from del pezzo surfaces with picard rank one

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

doi:10.1090/tran/8119

Anticanonical codes from del pezzo surfaces with picard rank one

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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	5371-5393
Number of pages	23
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	8
DOIs	https://doi.org/10.1090/tran/8119
Publication status	Published - 1 Aug 2020

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10.1090/tran/8119

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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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AU - Blache, Régis

AU - Couvreur, Alain

AU - Hallouin, Emmanuel

AU - Madore, David

AU - Nardi, Jade

AU - Rambaud, Matthieu

AU - Randriam, Hugues

PY - 2020/8/1

Y1 - 2020/8/1

N2 - 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.

AB - 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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DO - 10.1090/tran/8119

M3 - Article

AN - SCOPUS:85090217940

SN - 0002-9947

VL - 373

SP - 5371

EP - 5393

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -

Anticanonical codes from del pezzo surfaces with picard rank one

Abstract

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