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.