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Evaluation codes from smooth quadric surfaces and twisted Segre varieties

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Abstract

We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH structure on these codes and using the BCH bound. The elliptic quadric is a twist of the surface P 1 × P 1 and we detect a similar BCH structure on twists of the Segre embedding of a product of any d copies of the projective line.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux, Université Bordeaux I, 351, cours de la Libération, Talence Cedex, 33405, France

    Alain Couvreur

  2. Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green Street (MC-382), Urbana, IL, 61801-2975, USA

    Iwan Duursma

Authors
  1. Alain Couvreur
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  2. Iwan Duursma
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Correspondence to Alain Couvreur.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

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Couvreur, A., Duursma, I. Evaluation codes from smooth quadric surfaces and twisted Segre varieties. Des. Codes Cryptogr. 66, 291–303 (2013). https://doi.org/10.1007/s10623-012-9692-4

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  • DOI: https://doi.org/10.1007/s10623-012-9692-4

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