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

Alain Couvreur 1, 2 
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : In this article, the minimum distance of the dual of a functional code on an arbitrary dimensional variety X over a finite field 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.
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Submitted on : Thursday, November 10, 2011 - 11:37:16 PM
Last modification on : Saturday, June 25, 2022 - 7:43:06 PM
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Alain Couvreur. The dual minimum distance of arbitrary-dimensional algebraic-geometric codes. Journal of Algebra, Elsevier, 2012, 350 (1), pp.84-107. ⟨10.1016/j.jalgebra.2011.09.030⟩. ⟨inria-00540022v3⟩

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