Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties
Information Theory
2013-09-18 v3 Algebraic Geometry
math.IT
Number Theory
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.
Keywords
Cite
@article{arxiv.1101.4603,
title = {Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties},
author = {Alain Couvreur and Iwan Duursma},
journal= {arXiv preprint arXiv:1101.4603},
year = {2013}
}
Comments
10 pages. Presented at the conference Workshop on Coding theory and Cryptography 2011