Uma melhora das cotas de Feng-Rao e de Miura para a distância mínima de códigos definidos sobre uma variedade afim

• Autor(a) principal: MESQUITA, Aline Mota de
• Data de Publicação: 2007
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000d3qf
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tde/1962
• topic: Códigos Lineares Código Geométrico de Goppa Cota de Feng-Rao Cota de Miura Álgebra; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we present some linear codes and we discuss about parameters of cyclic codes families that lead to the characterization of the Goppa codes, which we describe minimum distance bounds when it is given for an affine variety. When this code is defined like this, we say that it is an improved geometric Goppa code. The first bounds mentioned in this work was given by Feng and Rao in [6] (Feng-Rao bound), later improved by Miura in [18],[19] (weakly Feng-Rao bound), that in its turn has been improved by G. Salazar, D. Dunn and S. B. Graham in [22] (advisory bound and strong advisory estimate). This work was based in this last article. We finishing the dissertation showing families of codes for which we verified the veracity of the improvement of bounds.