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| HAL : hal-00707540, version 1 |
| DOI : 10.1007/s10623-012-9692-4 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Designs, Codes and Cryptography 66, 1-3 (2013) 291-303 |
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| Evaluation codes from smooth quadric surfaces and twisted Segre varieties |
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Alain Couvreur 1Iwan Duursma 2 |
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| (01/01/2013) |
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| 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 P1 × P1 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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| 1 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2 : | University of Illinois at Urbana{Champaign Department of Mathematics |
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University of Illinois at Urbana{Champaign Department of Mathematics |
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| Domaine | : | Mathématiques/Géométrie algébrique Mathématiques/Théorie de l'information et codage Informatique/Théorie de l'information et codage Mathématiques/Théorie des nombres |
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| Evaluation codes – Algebraic Geometry codes – quadric surfaces – BCH codes – Segre embedding. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00707540, version 1 | |
| http://hal.inria.fr/hal-00707540 | |
| oai:hal.inria.fr:hal-00707540 | |
| Contributeur : Alain Couvreur | |
| Soumis le : Mardi 12 Juin 2012, 23:22:34 | |
| Dernière modification le : Mardi 23 Avril 2013, 16:08:13 | |
