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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • Régis Blache
  • Affiliation: LAMIA, Université des Antilles, BP592, 97159 Pointe-â-Pitre Cedex, Guadeloupe
  • Email: regis.blache@univ-antilles.fr
  • Alain Couvreur
  • Affiliation: INRIA & Laboratoire LIX, CNRS UMR 7161, École Polytechnique, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
  • MR Author ID: 883516
  • Email: alain.couvreur@inria.fr
  • Emmanuel Hallouin
  • Affiliation: Institut de Mathématiques de Toulouse, UMR 5219, Université Paul Sabatier, 118, Route de Narbonne, F-31062 Toulouse Cedex 9, France
  • MR Author ID: 682863
  • Email: hallouin@univ-tlse2.fr
  • David Madore
  • Affiliation: LTCI Telecom ParisTech, 19 Place Marguerite Perey, 91120 Palaiseau, France
  • MR Author ID: 665712
  • Email: david.madore@telecom-paristech.fr
  • Jade Nardi
  • Affiliation: Institut de Mathématiques de Toulouse, UMR 5219, Université Paul Sabatier, 118, Route de Narbonne, F-31062 Toulouse Cedex 9, France
  • MR Author ID: 1333013
  • ORCID: 0000-0003-0901-7266
  • Email: jade.nardi@inria.fr
  • Matthieu Rambaud
  • Affiliation: LTCI Telecom ParisTech, 19 Place Marguerite Perey, 91120 Palaiseau, France
  • MR Author ID: 1119481
  • Email: matthieu.rambaud@telecom-paristech.fr
  • Hugues Randriam
  • Affiliation: LTCI Telecom ParisTech, 19 Place Marguerite Perey, 91120 Palaiseau, France
  • Address at time of publication: ANSSI, Laboratoire de Cryptographie, Tour Mercure, 31 quai de Grenelle 75015 Paris, France
  • MR Author ID: 684200
  • Email: randriam@telecom-paristech.fr
  • Received by editor(s): April 18, 2019
  • Received by editor(s) in revised form: August 7, 2019
  • Published electronically: May 26, 2020
  • Additional Notes: The authors have been funded by ANR project ANR-15-CE39-0013 Manta
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 5371-5393
  • MSC (2010): Primary 14G50, 14J26, 94B27
  • DOI: https://doi.org/10.1090/tran/8119
  • MathSciNet review: 4127880