The dual minimum distance of arbitrary-dimensional algebraic–geometric codes

In this article, the minimum distance of the dual C ⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field F q is studied. The approach is based on problems à la Cayley–Bacharach and consists in describing the minimal configurations of points on X which fail to impose ind...

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Bibliographic Details
Published inJournal of algebra Vol. 350; no. 1; pp. 84 - 107
Main Author Couvreur, Alain
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2012
Elsevier
Subjects
Algebraic Geometry
Algebraic–geometric codes
Computer Science
Error-correcting codes
Finite fields
Information Theory
Linear systems
Mathematics
Finite fields
Linear systems
Algebraic–geometric codes
14C20
94B27
Error-correcting codes
14J20
Algebraic geometry
Codes géométriques
Systèmes linéaires de courbes
Géométrie algébrique
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Summary:In this article, the minimum distance of the dual C ⊥ of a functional code C on an arbitrary-dimensional variety X over a finite field F q is studied. The approach is based on problems à la Cayley–Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some degree m. If X is a curve, the result improves in some situations the well-known Goppa designed distance.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2011.09.030