Cyclic codes over the binary field, an exposition

• Main Author: Francisco, Gence-Ross Sanchez
• Format: text
• Language: English
• Published: Animo Repository 2002
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17201
• Institution: De La Salle University

This paper studies the full nature of cyclic codes over the binary field. Several concepts and theories about coding theory are introduced in order to comprehend better how cyclic codes work. Encoding and finding cyclic codes as well as the check polynomial and the idempotent of a cycle code are further discussed. Moreover, a preliminary review on groups, rings, fields, vector space, and matrices are essential to refresh the knowledge of the reader in linear and abstract algebra. A number of examples per topic are thoroughly discussed to give the reader an apparent idea on the complex matters involved in cyclic codes. Several Mathematics notebooks are programmed in order to picture some of the examples involved in the study. It is at least anticipated that this paper would be of big help to other researchers willing to partake a study in coding theory.