Praktické aplikace teoretické algebry

Abstract

This bachelor thesis deals with practical applications of Abstract Algebra. Error correcting codes are chosen as an application of Abstract Algebra. In this thesis, we look into selected applications where error correcting codes are used to detect and correct errors. Error correcting codes are considered to be an important part of many applications, especially where there is data transfer between sender and receiver. Interference or loss may occur during the transmission itself, and one solution may be to use error correcting codes that are able to detect and correct errors on the receiver side.

The aim of this thesis is to describe selected applications and how they specifically use error correcting codes in their operation. We describe parameters and properties for selected error correcting codes. We describe the function of error correcting codes, the process of encoding, decoding and the actual error correction. For some of the error correcting codes, examples are provided to demonstrate each encoding and decoding procedures. We will also highlight some of the differences between the error correcting codes used in real life applications.

The work is primarily a survey, working with a number of sources is expected. We compare various sources and select appropriate passages applicable to this work.