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

✍ Scribed by Jiri Adamek(auth.)

• Year: 1991
• Tongue: English
• Leaves: 335
• Category: Library

✦ Synopsis

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):