Elements of Algebraic Coding Systems

Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' 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.

Valdemar Cardoso da Rocha Jr. received his BSc degree in electrical and electronics engineering from the Escola Politecnica, Recife, Brazil, in 1970; and his PhD degree in electronics from the University of Kent at Canterbury, England, in 1976. In 1976, he joined the faculty of the Federal University of Pernambuco, Recife, Brazil, as an Associate Professor and founded the Electrical Engineering Postgraduate Program. He has been a consultant to both the Brazilian Ministry of Education and the Ministry of Science and Technology on postgraduate education and research in electrical engineering. He was the Chairman of the Electrical Engineering Committee in the Brazilian National Council for Scientific and Technological Development for two terms. He is a founding member, former President, and Emeritus Member of the Brazilian Telecommunications Society. He is also a Life Senior Member of the IEEE Communications Society and the IEEE Information Theory Society and a Fellow of the Institute of Mathematics and its Applications."