Álgebra de corpos finitos aplicada à teoria da codificação: estudo do codificador BCH.

Abstract

This work aims to study the application of abstract mathematics in Coding Theory, through the study of error correcting codes and a sepcial class denoted BCH. The BCH code building uses algebraic structure of finite fields and are characterized by operations on polynomials. In order to understand the operation of the BCH codes, we will make a brief introduction to the study of rings, fields, congruence relations on the integers, polynomial rings, Galois fields, and vector spaces. Next, we’ll be introduced the linear block codes and cyclic codes, and ultimately a special class of cyclic codes known as BCH.