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. 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
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
