It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book.
When the second edition was prepared， only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction， the chapter requires more mathematical background of the reader than the remainder of this book.
One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 24. There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 24-codes.
Furthermore， some material has been added that appeared in my Springer Lecture Notes 201， but was not included in earlier editions of this book， e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2， a section on \"Coding Gain\"（the engineer's justification for using error-correcting codes）was added.
It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book.
When the second edition was prepared， only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction， the chapter requires more mathematical background of the reader than the remainder of this book.
One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 24. There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 24-codes.
Furthermore， some material has been added that appeared in my Springer Lecture Notes 201， but was not included in earlier editions of this book， e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2， a section on \"Coding Gain\"（the engineer's justification for using error-correcting codes）was added.
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
CHAPTER I Mathematical Background
1．1．Algebra
1．2．Krawtchouk Polynomials
1．3．Combinatorial Theory
1．4．Probability Theory
CHAPTER 2 Shannon's Theorem
2．1．Introduction
2．2．Shannon's Theorem
2．3．On Coding Gain
2．4．Comments
2．5．Problems
CHAPTER 3 Linear Codes
3．1．Block Codes
3．2．Linear Codes
3．3．Hamming Codes
3．4．Majority Logic Decoding
3．5．Weight Enumerators
3．6．The Lee Metric
3．7．Comments
3．8．Problems
……
CHAPTER 4 Some Good Codes
CHAPTER 5 Bounds on Codes
CHAPTER 6 Cyclic Codes
CHAPTER 7 Perfect Codes and Uniformly Packed Codes
CHAPTER 8 Codes over 24
CHAPTER 9 Goppa Codes
CHAPTER 10 Algebraic Geometry Codes
CHAPTER 11 Asymptotically Good Algebraic Codes
CHAPTER 12 Arithmetic Codes
CHAPTER 13 Convolutional Codes
Hints and Solutions to Problems
References
Index
书单推荐
