Fast decoding of dual multipoint codes from algebraic curves up to the Kirfel-Pellikaan bound

Masaya Fujisawa (1) , Shojiro Sakata (2)

1 Tokyo University of Science [Tokyo]
2 The University of Electro-Communications [Tokyo]

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]

Masaya Fujisawa, Shojiro Sakata. Fast decoding of dual multipoint codes from algebraic curves up to the Kirfel-Pellikaan bound. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01275736⟩