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

JOURNAL OF ALGEBRA

卷:350

Article

Couvreur, Alain

关键词: Algebraic geometry;    Finite fields;    Error-correcting codes;    Algebraic-geometric codes;    Linear systems;   

DOI  :  10.1016/j.jalgebra.2011.09.030

来源: Elsevier

【 摘 要 】

In this article, the minimum distance of the dual C-perpendicular to 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 a 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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