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Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties (1101.4603v3)
Published 24 Jan 2011 in cs.IT, math.AG, math.IT, and math.NT
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 P1 x 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.