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

Abstract : 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.
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Pascale Charpin, Nicolas Sendrier, Jean-Pierre Tillich. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Apr 2015, Paris, France. 2016, Proceedings of the 9th International Workshop on Coding and Cryptography 2015 WCC2015
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Masaya Fujisawa, Shojiro Sakata. Fast decoding of dual multipoint codes from algebraic curves up to the Kirfel-Pellikaan bound. Pascale Charpin, Nicolas Sendrier, Jean-Pierre Tillich. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Apr 2015, Paris, France. 2016, Proceedings of the 9th International Workshop on Coding and Cryptography 2015 WCC2015. 〈hal-01275736〉

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