Skip to Main content Skip to Navigation
Journal articles

Differential Approach for the Study of Duals of Algebraic-Geometric Codes on Surfaces

Alain Couvreur 1
1 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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.
Complete list of metadata

https://hal.inria.fr/inria-00541894
Contributor : Alain Couvreur <>
Submitted on : Wednesday, December 1, 2010 - 6:01:49 PM
Last modification on : Monday, March 1, 2021 - 11:29:27 AM
Long-term archiving on: : Wednesday, March 2, 2011 - 2:31:16 AM

File

couvreur_differential_approach...
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00541894, version 1

Collections

Citation

Alain Couvreur. Differential Approach for the Study of Duals of Algebraic-Geometric Codes on Surfaces. Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2011, 23 (1), pp.95-120. ⟨inria-00541894⟩

Share

Metrics

Record views

476

Files downloads

602