52 citations · 134 across the 30 of their papers we have counts for
9 papers · 1 filter
A proof of the Brill-Noether method from scratch
Elena Berardini, Alain Couvreur, Grégoire Lecerf
In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being…
How arithmetic and geometry make error correcting codes better
Alain Couvreur
This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Fini…
Toward good families of codes from towers of surfaces
Alain Couvreur, Philippe Lebacque, Marc Perret
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and tu…
Anticanonical codes from del Pezzo surfaces with Picard rank one
Régis Blache, Alain Couvreur, Emmanuel Hallouin +4
We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit co…
An upper bound on the number of rational points of arbitrary projective varieties over finite fields
Alain Couvreur
We give an upper bound on the number of rational points of an arbitrary Zariski closed subset of a projective space over a finite field. This bound depends only on the dimensions a…
Construction of Rational Surfaces Yielding Good Codes
Alain Couvreur
In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane cu…
The dual minimum distance of arbitrary dimensional algebraic--geometric codes
A. Couvreur
In this article, the minimum distance of the dual of a functional code on an arbitrary dimensional variety over a finite field $\F_q$ is studied. The approach co…
Differential approach for the study of duals of algebraic-geometric codes on surfaces
A. Couvreur
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 t…
Sums of residues on algebraic surfaces and application to coding theory
Alain Couvreur
In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using…