Goppa geometry codes via elementary methods / Codigos geometricos de Goppa via metodos elementares




The central objective of this dissertation was to present the Goppa Geometry Codes via elementary methods which were introduced by J. H. van Lint, R. Pellikaan and T. Hfhold about 1998. On the first past of such dissertation are presented the fundamental concepts about fields of rational functions of an algebraic curve in the direction as to define the Goppa Codes on a classical manner. In this study we based ourselves mainly on the book ?Algebraic Function Fields and Codes? of H. Stichtenoth. The second part is initiated with an introduction about the functions weight, degree and order which are fundamental for the study of the Goppa Codes throught elementary methods of linear algebra and of semigroups and such study was based on ?Algebraic Geometry Codes? of J. h. van Lint, R. Pellikaan and T. Hfhold. The dissertation ends up with a presentation of examples which illustrate the elementary methods that we have referred to above


codigos de controle de erros (teoria da informação) geometria algebrica semigrupos coding theory error control codes (information theory) algebraic geometry teoria da codificação semigroups

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