Limitantes para Códigos de Peso Constante

• Autor(a) principal: RODRIGUES, Silvana da Silva
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tde/1935
• topic: Raio de Cobertura; Limitantes Superiores e Inferiores; Códigos Corretores de Erros; Totobola; Piscina de Futebol; 1.Álgebra linear 2.Teoria de códigos 3.Códigos lineares 4.Código de correção de erros; covering radius; upper and lower bounds; error correcting codes; totobola; football pool; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

The main purpose of this dissertation was to construct lower and upper bounds for the cardinality of the error correcting codes for constant-weight, contained in the vector space Fn 3 , where F3 is a field with three elements, knowing parameters such as length and minimum distance code. We present the main results of linear algebra necessary to develop the theory of codes and then the fundamental concepts of more practical class of codes, the linear error correcting codes. We state the Totobola problem and the Football problem, relating them to the theory of codes and present some bounds for the "covering radius problem"for r = 1 , some values of n. In the last chapter, we conclude the work with some examples that illustrate bounds of coverings for Fn 3 , with r = 2 and 3, and the generalization of the problem, where we present the binary covering radius problem, the case of multiple coverages and the extension of the idea, citing bounds for the cardinality of the codes contained in the vector space over a finite field with any arbitrary number of elements.