Corpos finitos: códigos cíclicos e BCH binário

Abstract

Because of the increasing use of data trasmission, it was important to create methods to ensure that the information received
was equivalent to the information sended. In this context it was created Error-control codes that are used to detect and correct
errors that can occur during data transmission. These are now indispensable in the transmission of digital information. One
of the first codes created for this purpose was formulated in the 1940s by Richard Hamming. Besides Hamming’s code,
other types were created to correct and detect errors. Among these types are cyclic codes. Such codes include a variety
of particular codes, such as the Reed Solomon (RS) and the Bose-Chaudhuri-Hocquenghem (BCH code). In this sense, the
paper discusses general concepts of cyclic codes relying on finite body theory. In addition, it presents the definition of the
BCH code, showing an example that goes through the encoding of information and its decoding. Thereby, this article showed
an application of Finite Fields and Abstract Algebra.