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.