Detalhes bibliográficos
| Ano de defesa: |
2021 |
| Autor(a) principal: |
Matos, Rayanne Auxiliadora de Oliveira
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| Orientador(a): |
Silva, Jhone Caldeira
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| Banca de defesa: |
Silva, Jhone Caldeira,
Chaves, Ana Paula de Araújo,
Lelis, Jean Carlos de Aguiar |
| Tipo de documento: |
Dissertação
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| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Universidade Federal de Goiás
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| Programa de Pós-Graduação: |
PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)
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| Departamento: |
Instituto de Matemática e Estatística - IME (RG)
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| País: |
Brasil
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| Palavras-chave em Português: |
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| Palavras-chave em Inglês: |
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| Área do conhecimento CNPq: |
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| Link de acesso: |
http://repositorio.bc.ufg.br/tede/handle/tede/11299
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Resumo: |
In this paper the basic concepts for the construction of Error-Correcting Codes will be presented. In particular, the construction of Linear Codes and a brief introduction to the construction of Geometric Algebraic Codes. Such codes are used to ensure the reliability of messages sent over long distances, over different channels, so it is necessary to have ways to detect and correct errors. We begin by discussing the mathematical tools needed to construct the different codes. We present the fundamentals of the Theory of Error-Correcting Codes, and present how to construct the generator and decoder matrices of a code. In particular, we also present Cyclic Codes, BCH Codes, and Rational Goppa Codes, with their generator and decoder matrices. We also present Algebraic Functions Fields over Finite Fields, because these are of great interest for Code Theory, since with this theory it is possible to construct Geometric Algebraic Codes, a subject that we address in an introductory way at the end of the text and, for which, we indicate some possibilities for future studies. |
