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

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.