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.Content:
Chapter 1 Coding and Decoding (pages 3–16):
Chapter 2 Huffman Codes (pages 17–24):
Chapter 3 Data Compression and Entropy (pages 25–38):
Chapter 4 Reliable Communication Through Unreliable Channels (pages 39–60):
Chapter 5 Binary Linear Codes (pages 61–78):
Chapter 6 Groups and Standard Arrays (pages 79–89):
Chapter 7 Linear Algebra (pages 91–114):
Chapter 8 Linear Codes (pages 115–135):
Chapter 9 Reed?Muller Codes: Weak Codes with Easy Decoding (pages 137–160):
Chapter 10 Cyclic Codes (pages 161–195):
Chapter 11 Polynomials and Finite Fields (pages 197–227):
Chapter 12 BCH Codes: Strong Codes Correcting Multiple Errors (pages 229–256):
Chapter 13 Fast Decoding of BCH Codes (pages 257–267):
Chapter 14 Convolutional Codes (pages 269–290):
Chapter 15 Cryptography (pages 291–317):