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

Abstract

In this article, the minimum distance of the dual $C^{\perp }$ 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.

24 pages

References in corpus (1)

• Residus de 2-formes differentielles sur les surfaces algebriques et applications aux codes correcteurs d'erreurs

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• Rational points on cubic surfaces and AG codes from the Norm-Trace curve
• Multi-point Codes from Generalized Hermitian Curves
• Codes over a weighted torus
• On the minimum distance and the minimum weight of Goppa codes from a quotient of the Hermitian curve
• On the Hermitian curve, its intersections with some conics and their applications to affine-variety codes and Hermitian codes
• Sets computing the symmetric tensor rank
• The dual geometry of Hermitian two-point codes
• Explicit Construction of AG Codes from Generalized Hermitian Curves
• Differential Codes on Higher Dimensional Varieties Via Grothendieck's Residue Symbol