Evaluation codes from smooth quadric surfaces and twisted Segre varieties

Alain Couvreur; Iwan Duursma

doi:10.1007/s10623-012-9692-4

Evaluation codes from smooth quadric surfaces and twisted Segre varieties

Alain Couvreur
, Iwan Duursma

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	291-303
Number of pages	13
Journal	Designs, Codes, and Cryptography
Volume	66
Issue number	1-3
DOIs	https://doi.org/10.1007/s10623-012-9692-4
Publication status	Published - 1 Jan 2013
Externally published	Yes

Keywords

Algebraic geometry codes
BCH codes
Evaluation codes
Quadric surfaces
Segre embedding

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10.1007/s10623-012-9692-4

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title = "Evaluation codes from smooth quadric surfaces and twisted Segre varieties",

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.",

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AB - 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.

KW - Algebraic geometry codes

KW - BCH codes

KW - Evaluation codes

KW - Quadric surfaces

KW - Segre embedding

U2 - 10.1007/s10623-012-9692-4

DO - 10.1007/s10623-012-9692-4

M3 - Article

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SN - 0925-1022

VL - 66

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JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 1-3

ER -

Evaluation codes from smooth quadric surfaces and twisted Segre varieties

Abstract

Keywords

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