Evaluation codes from smooth quadric surfaces and twisted Segre varieties

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 qua...

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Bibliographic Details
Published inDesigns, codes, and cryptography Vol. 66; no. 1-3; pp. 291 - 303
Main Authors Couvreur, Alain, Duursma, Iwan
Format Journal Article
LanguageEnglish
Published Boston Springer US 2013
Springer Verlag
Subjects
Algebraic Geometry
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Information Theory
Mathematics
Number Theory
94B15
Segre embedding
Evaluation codes
Quadric surfaces
94B27
Algebraic geometry codes
BCH codes
14J20
Algebraic Geometry codes
quadric surfaces
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Summary: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 P 1 × 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.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-012-9692-4