Differential approach for the study of duals of algebraic-geometric codes on surfaces
Algebraic Geometry
2011-09-14 v4 Information Theory
math.IT
Number Theory
Abstract
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code on a curve is a differential code. We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples of codes on surfaces, and in particular surfaces with Picard number 1 like elliptic quadrics or some particular cubic surfaces. The parameters of some of the studied codes reach those of the best known codes up to now.
Keywords
Cite
@article{arxiv.0905.2341,
title = {Differential approach for the study of duals of algebraic-geometric codes on surfaces},
author = {A. Couvreur},
journal= {arXiv preprint arXiv:0905.2341},
year = {2011}
}
Comments
21 pages