Introduction to Coding Theory

Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory, Second Edition introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, the linear programming bound, quantum codes, and the geometric description of codes, as well as a self-contained Production to linear programming. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. As well as revisions to bring its existing chapters up-to-dale with the latest developments in the field, this new and enhanced edition now includes a section dedicated to the theory of algebraic curves and its most important applications to coding theory, as well as now exercises throughout the text as a whole. Book jacket.