Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties

Details Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties

2011-01-24

arxiv.org/abs/1101.4603v2

Computer Science

Information Theory

10 pages. Presented at the conference Workshop on Coding theory and Cryptography 2011

Scientific paper

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 of these codes and using the BCH bound. The elliptic quadric is a twist of the surface P^1 x 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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