Generalization of the Lee-O'Sullivan list decoding for one-point AG codes

Matsumoto, Ryutaroh; Ruano Benito, Diego; Geil, Olav

doi:10.1016/j.jsc.2013.03.001

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Título

Generalization of the Lee-O'Sullivan list decoding for one-point AG codes

Autor

Matsumoto, Ryutaroh

Ruano Benito, Diego

Geil, Olav

Año del Documento

2013

Descripción

Producción Científica

Documento Fuente

Journal of Symbolic Computation. Volume 55, pages 1-9 (2013)

Resumen

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gröbner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables us to apply the fast algorithm to compute a Gröbner basis of a module proposed by Lee and O'Sullivan, which was not possible in another generalization by Lax.

Revisión por pares

DOI

10.1016/j.jsc.2013.03.001

Patrocinador

This research was partly supported by the MEXT Grant-in-Aid for Scientific Research (A) No. 23246071, the Villum Foundation through their VELUX Visiting Professor Programme 2011--2012, the Danish National Research Foundation and the National Science Foundation of China (Grant No. 11061130539) for the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography and by Spanish grant MTM2007-64704 and by Spanish MINECO grant No. MTM2012-36917-C03-03