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Evaluation codes from smooth quadric surfaces and twisted Segre varieties |
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| Authors: | Alain Couvreur Iwan Duursma |
| Institution: | 1. Institut de Mathématiques de Bordeaux, Université Bordeaux I, 351, cours de la Libération, Talence Cedex, 33405, France 2. Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green Street (MC-382), Urbana, IL, 61801-2975, USA |
| 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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