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

Alain Couvreur 1 
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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.
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Submitted on : Wednesday, December 1, 2010 - 6:01:49 PM
Last modification on : Friday, February 4, 2022 - 3:34:29 AM
Long-term archiving on: : Wednesday, March 2, 2011 - 2:31:16 AM


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  • HAL Id : inria-00541894, version 1



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⟩



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