Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel

Irene Ndanu John

doi:10.11648/j.pamj.20160506.17

Abstract

This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction schemes of hamming and cyclic codes.

Highlights

Coding theory is concerned with the transmission of data across noisy channels and the recovery of corrupted messages, Altaian [1]
While the problems in coding theory often arise from engineering applications, it is fascinating to note the crucial role played by mathematics in the development of the field
General Objective The main objective of this study was to provide an overview of two types of linear block codes: Hamming and cyclic codes and study schemes and/or algorithms of error detection and correction of these codes

Summary

Introduction

Coding theory is concerned with the transmission of data across noisy channels and the recovery of corrupted messages, Altaian [1]. It has found widespread applications in electrical engineering, digital communication, Mathematics and computer science. While the problems in coding theory often arise from engineering applications, it is fascinating to note the crucial role played by mathematics in the development of the field. An algebraic techniques involving finite fields, group theory, polynomial algebra as well as linear algebra deal with the design of error-correcting codes for the reliable transmission of information across noisy channels. The importance of algebra in coding theory is a commonly acknowledged fact, with many deep mathematical results being used in elegant ways in the advancement of coding theory; coding theory appeals not just to engineers and computer scientists, and to mathematicians and coding theory is sometimes called algebraic coding theory, Doran [3].

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Conclusion