Foundations of Coding: Theory and Applications of Error–Correcting Codes with an Introduction to Cryptography and Information Theory

Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error–detecting and error–correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error–correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition–theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.

Spis treści:
CODING AND INFORMATION THEORY.
Coding and Decoding.
Huffman Codes.
Data Compression and Entropy.
Reliable Communication Through Unreliable Channels.
ERROR–CORRECTING CODES.
Binary Linear Codes.
Groups and Standard Arrays.
Linear Algebra.
Linear Codes.
Reed–Muller Codes: Weak Codes with Easy Decoding.
Cyclic Codes.
Polynomials and Finite Fields.
BCH Codes: Strong Codes Correcting Multiple Errors.
Fast Decoding of BCH Codes.
Convolutional Codes.
CRYPTOGRAPHY.
Cryptography.
Appendices.
Bibliography.
List of Symbols.
Index.