Fast decoding of dual multipoint codes from algebraic curves up to the Kirfel-Pellikaan bound
Résumé
Multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions which have multiple poles/zeros on their defining curves. The one-point codes which are viewed as its subclass can be decoded efficiently up to the Feng-Rao bound by using the BMS algorithm with majority logic [1]. Recently we published [2] a fast method for decoding primal multipoint codes from curves based on the vectorial BMS algorithm [3]. Although the simulation shows that the method can correct most error patterns of weight up to 1/2 d_G, it is guaranteed theoretically that every error of weight only up to 1/2 (d_G − g) can be corrected, where g is the genus of the defining curve. In this paper we present a fast method for decoding dual multipoint codes from algebraic curves up to the Kirfel-Pellikaan bound, based on the vectorial BMS algorithm with majority logic.
Domaines
Théorie de l'information [cs.IT]
Origine : Fichiers produits par l'(les) auteur(s)
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