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

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

2009-05-14

arxiv.org/abs/0905.2345v3

Mathematics

Algebraic Geometry

24 pages

Scientific paper

10.1016/j.jalgebra.2011.09.030

In this article, the minimum distance of the dual $C^{\bot}$ of a functional
code $C$ on an arbitrary dimensional variety $X$ over a finite field $\F_q$ is
studied. The approach consists in finding minimal configurations of points on
$X$ which are not in "general position". If $X$ is a curve, the result improves
in some situations the well-known Goppa designed distance.

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