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Evaluation Codes from Smooth Quadric Surfaces and Twisted Segre Varieties

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 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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https://hal.inria.fr/inria-00611801
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Submitted on : Wednesday, July 27, 2011 - 3:07:42 PM
Last modification on : Thursday, August 1, 2019 - 2:12:06 PM

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  • HAL Id : inria-00611801, version 1

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Alain Couvreur, Iwan Duursma. Evaluation Codes from Smooth Quadric Surfaces and Twisted Segre Varieties. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.243-252. ⟨inria-00611801⟩

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