Evaluation codes from smooth quadric surfaces and twisted Segre varieties

Alain Couvreur, Iwan Duursma

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Pages (from-to)291-303
Number of pages13
JournalDesigns, Codes, and Cryptography
Volume66
Issue number1-3
DOIs
StatePublished - Jan 2013

Keywords

  • Algebraic geometry codes
  • BCH codes
  • Evaluation codes
  • Quadric surfaces
  • Segre embedding

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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