Elements of Algebraic Coding Systems

This book aims to serve as an introductory text on algebraic coding theory. The contents are suitable for a final year undergraduate and beginning graduate course in Electrical Engineering. The material will give the reader knowledge of coding fundamentals essential for a deeper understanding of state-of-the-art coding systems. This book will also serve as a quick reference for students or practitioners who have not been exposed to the topic, but need it for specific applications such as cryptography and communications. The book will cover linear error-correcting block codes from elementary principles, going through cyclic codes and then covering some finite field algebra, Goppa codes, algebraic decoding algorithms and applications in public-key cryptography and private-key cryptography. Three appendices will cover the Gilbert bound and some related derivations, a derivation of the Mac Williamsâe(tm) identities based on the probability of undetected error, and the finite field Fourier transform and the Euclidean algorithm for polynomials.