Coding Theory

Abstract

This work presents a structured study of coding theory, focusing on both the theoretical foundations and the practical aspects of code constructionandanalysis. Beginningwiththebasicmathematicalcon- cepts underlying error-control coding, we explore linear block codes, the main coding theory problem, and specific code families, such as Hammingandcycliccodes. Eachtopicissupportedbydetailedworked examplesandobservationstoillustratetheencodinganddecodingpro- cesses in a clear and accessible manner. The goal is to bridge the gap between abstract algebraic formulations and their direct applications to real-world communication systems to ensure reliable data transmis- sionovernoisychannels. Theresultsandexamplespresentedprovidea learning resource and foundation for further research in more advanced error-correcting codes.