Ebook: Elements of algebraic coding systems
Author: Valdemar Cardosa da Rocha
- Tags: Coding theory, Algebraic coding, Algebraic fields, Curves Elliptic, SCIENCE, System Theory, TECHNOLOGY & ENGINEERING, Operations Research, codes, BCH codes, Goppa codes, decoding, majority logic decoding, time domain decoding, frequency domain decoding, Finite fields, polynomial factorization, error-correcting codes, algebraic codes, cyclic
- Series: Communications and signal processing collection
- Year: 2014
- Publisher: Momentum Press
- Language: English
- pdf
This book serves as an introductory text to algebraic coding theory. The contents are suitable for final year undergraduate and first year graduate courses in electrical and computer engineering, and will give the reader knowledge of coding fundamentals that is essential for a deeper understanding of state-of-the-art coding systems. This book will also serve as a quick reference for those who need it for specificRead more...
Abstract: This book serves as an introductory text to algebraic coding theory. The contents are suitable for final year undergraduate and first year graduate courses in electrical and computer engineering, and will give the reader knowledge of coding fundamentals that is essential for a deeper understanding of state-of-the-art coding systems. This book will also serve as a quick reference for those who need it for specific applications, like in cryptography and communications. Eleven chapters 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 secret-key cryptography. At the end of each chapter a section containing problems and solutions is included. Three appendices cover the Gilbert bound and some related derivations, a derivation of the MacWilliams' identities based on the probability of undetected error, and two important tools for algebraic decoding, namely, the finite field Fourier transform and the Euclidean algorithm for polynomials