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Decodificação de lista para códigos de F. K. Schmidt usando Bases de Grobner

Taciana A. Souza, Francisco M. Assis, Leocarlos B. S. Lima
Algebraic geometric codesList decodingF. K. Schmidt curveGrobner basis

Resumo

F. K. Schmidt codes are algebraic geometric codes that consist on a generalization of Hermitian codes. In this paper, a list decoding algorithm for F. K. Schmidt codes is presented, which yields better performance than single decoding algorithms, that are less flexible. The presented algorithm employs Grobner ¨ basis on modules and is a generalization of an algorithm proposed by Lee and O’Sullivan, in 2009, for Hermitian codes.