Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties

Alain Couvreur; Iwan Duursma

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arXiv · 1101.4603

Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties

Alain Couvreur·Iwan Duursma

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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 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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Alain Couvreur, Iwan Duursma. 2011-01-24. Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties. https://arxiv.org/abs/1101.4603

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