Goppa goemetry codes via elementary methods (In Portuguese) (1204.1559v1)

Abstract: 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. Hohold about 1998. On the first part of such dissertation are presented the fundamental concepts about bodies 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 through 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. Hohold.