Goppa goemetry codes via elementary methods (In Portuguese)

TL;DR

This paper presents Goppa Geometry Codes using elementary methods based on linear algebra and semigroups, aiming to make the concepts more accessible and straightforward compared to traditional approaches.

Contribution

It introduces an elementary approach to Goppa Codes, simplifying their understanding by relying on basic linear algebra and semigroup theory, inspired by works of van Lint, Pellikaan, and Hohold.

Findings

Simplified construction of Goppa Codes using elementary methods

Clarification of fundamental concepts like function weight, degree, and order

Enhanced accessibility of algebraic geometry codes for students and researchers

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.