尽管市场上有关编码理论的书籍繁多，本书以其高品质脱颖而出，是编码理论相关书籍榜上畅销不衰的经典。本书特色在于：简短、精确、数学严谨地介绍了书本主题内容，从数学家的角度清晰地提出了基本概念和思想，并在各种特殊类型的代码中加以说明。本书被推崇为每个想要了解编码代数理论的数学家的必读之书。再版版本除了添加了编码增益等内容，还附上了关于编码理论的最新文献，让读者能够进一步拓展知识面。

Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
CHAPTER 1 Mathematical Background
1.1. Algebra
1.2. Krawtchouk Polynomials
1.3. Cormbinatorial 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
Some Good Codes
4.1. Hadamard Codes and Generalizations
4.2. The Binary Golay Code
4.3. The Ternary Golay Code
4.4. Constructing Codes from Other Codes
4.5. Reed-Muller Codes
4.6. Kerdock Codes
4.7. Comments
4.8. Problems
CHAPTER 5 Bounds on Codes
5.1. Introduction: The Gilbert Bound
5.2. Upper Bounds
5.3. The Linear Programming Bound
5.4. Comments
5.5. Problems
CHAPTER 6 Cyclic Codes
6.1. Definitions
6.2. Generator Matrix and Check Polynomial
6.3. Zeros of a Cyclic Code
6.4. The Idempotent of a Cyclic Code
6.5. Other Representations of Cyclic Codes
6.6. BCH Codes
6.7. Decoding BCH Codes
6.8. Reed-Solomon Codes
6.9. Quadratic Residue Codes
6.10. Binary Cyclic Codes of Length 2n(n odd)
6.11. Generalized Reed–Muller Codes
6.12. Comments
6.13. Problems
CHAPTER 7 Perfect Codes and Uniformly Packed Codes
7.1. Lloyd's Theorem
7.2. The Characteristic Polynomial of a Code
7.3. Uniformly Packed Codes
7.4. Examples of Unifomly Packed Codes
7.5. Nonexistence Theorems
7.6. Comments
7.7. Problems
CHAPTER 8 Codes over Z
8.1. Quaternary Codes
8.2. Binary Codes Derived from Codes over Z
8.3. Galois Rings over Z
8.4. Cyclic Codes over Z
8.5. Problems
CHAPTER 9 Goppa Codes
9.1. Motivation
9.2. Goppa Codes
9.3. The Minimum Distance of Goppa Codes
9.4. Asymptotic Behaviour of Goppa Codes
9.5. Decoding Goppa Codes
9.6. Generalized BCH Codes
9.7. Comments
9.8. Problems
CHAPTER 10 Algebraic Geometry Codes
10.1. Introduction
10.2. Algebraic Curves
10.3. Divisors
10.4. Differentials on a Curve
10.5. The Riemann-Roch Theorem
10.6. Codes from Algebraic Curves
10.7. Some Geometric Codes
10.8. Improvement of the Gilbert-Varshamov Bound
10.9. Comments
10.10. Problems
CHAPTER 11 Asymptotically Good Algebraic Codes
11.1. A Simple Nonconstructive Example
11.2. Justesen Codes
11.3. Comments
11.4. Problems
CHAPTER 12 Arithmetic Codes
12.1. AN Codes
12.2. The Arithmetic and Modular Weight
12.3. Mandelbaum-Barrows Codes
12.4. Comments
12.5. Problems
CHAPTER 13 Convolutional Codes
13.1. Introduction
13.2. Decoding of Convolutional Codes
13.3. An Analog of the Gilbert Bound for Some Convolutional Codes
13.4. Construction of Convolutional Codes from Cyclic Block Codes
13.5. Automorphisms of Convolutional Codes
13.6. Comments
13.7. Problems
Hints and Solutions to Problems
References
Index