Algebraic Geometric Codes on Surfaces
نویسندگان
چکیده
— We study error-correcting codes constructed from projective surfaces over finite fields using the generalized Goppa construction. We obtain bounds for the minimal distance of these codes by understanding how the zero sets of functions on a surface decompose into irreducible components. We also present a decoding algorithm for these codes based on the Luby-Mitzenmacher algorithm for LDPC codes. Résumé (Codes Algébriques Géométriques sur des surfaces). — Nous étudions les codes correcteurs d’erreurs construits à partir de surfaces projectives sur un corps fini, en utilisant la généralisation de la construction de Goppa. Nous obtenons des bornes pour la distance minimale de ces codes en étudiant comment les ensembles de zéros des fonctions sur une surface se décomposent en composantes irréductibles. Nous présentons également un algorithme de décodage pour ces codes fondé sur l’algorithme de Luby-Mitzenmacher pour les codes LDPC.
منابع مشابه
Differential approach for the study of duals of algebraic-geometric codes on surfaces
In this article, a differential construction for the dual of an algebraic-geometric code on a projective surface is given. Afterwards, this result is used to lower bound the minimum distance of this dual code. The found bounds involve intersection numbers of some particular divisors on the surface. AMS Classification: 14J20, 94B27, 11G25.
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