编码论导论 第3版PDF电子书下载

CHAPTER 1 Mathematical Background 1

1.1．Algebra 1

1.2．Krawtchouk Polynomials 14

1.3．Combinatorial Theory 17

1.4．Probability Theory 19

CHAPTER 2 Shannon's Theorem 22

2.1．Introduction 22

2.2．Shannon's Theorem 27

2.3．On Coding Gain 29

2.4．Comments 31

2.5．Problems 32

CHAPTER 3 Linear Codes 33

3.1．Block Codes 33

3.2．Linear Codes 35

3.3．Hamming Codes 38

3.4．Majority Logic Decoding 39

3.5．Weight Enumerators 40

3.6．The Lee Metric 42

3.7．Comments 44

3.8．Problems 45

CHAPTER 4 Some Good Codes 47

4.1．Hadamard Codes and Generalizations 47

4.2．The Binary Golay Code 48

4.3．The Ternary Golay Code 51

4.4．Constructing Codes from Other Codes 51

4.5．Reed-Muller Codes 54

4.6．Kerdock Codes 60

4.7．Comments 61

4.8．Problems 62

CHAPTER 5 Bounds on Codes 64

5.1．Introduction：The Gilbert Bound 64

5.2．Upper Bounds 67

5.3．The Linear Programming Bound 74

5.4．Comments 78

5.5．Problems 79

CHAPTER 6 Cyclic Codes 81

6.1．Definitions 81

6.2．Generator Matrix and Check Polynomial 83

6.3．Zeros of a Cyclic Code 84

6.4．The Idempotent of a Cyclic Code 86

6.5．Other Representations of Cyclic Codes 89

6.6．BCH Codes 91

6.7．Decoding BCH Codes 98

6.8．Reed-Solomon Codes 99

6.9．Quadratic Residue Codes 103

6.10．Binary Cyclic Codes of Length 2n（n odd） 106

6.11．Generalized Reed-Muller Codes 108

6.12．Comments 110

6.13．Problems 111

CHAPTER 7 Perfect Codes and Uniformly Packed Codes 112

7.1．Lloyd's Theorem 112

7.2．The Characteristic Polynomial of a Code 115

7.3．Uniformly Packed Codes 118

7.4．Examples of Uniformly Packed Codes 120

7.5．Nonexistence Theorems 123

7.6．Comments 127

7.7．Problems 127

CHAPTER 8 Codes over Z4 128

8.1．Quaternary Codes 128

8.2．Binary Codes Derived from Codes over Z4 129

8.3．Galois Rings over Z4 132

8.4．Cyclic Codes over Z4 136

8.5．Problems 138

CHAPTER 9 Goppa Codes 139

9.1．Motivation 139

9.2．Goppa Codes 140

9.3．The Minimum Distance of Goppa Codes 142

9.4．Asymptotic Behaviour of Goppa Codes 143

9.5．Decoding Goppa Codes 144

9.6．Generalized BCH Codes 145

9.7．Comments 146

9.8．Problems 147

CHAPTER 10 Algebraic Geometry Codes 148

10.1．Introduction 148

10.2．Algebraic Curves 149

10.3．Divisors 155

10.4．Differentials on a Curve 156

10.5．The Riemann-Roch Theorem 158

10.6．Codes from Algebraic Curves 160

10.7．Some Geometric Codes 162

10.8．Improvement of the Gilbert-Varshamov Bound 165

10.9．Comments 165

10.10．Problems 166

CHAPTER 11 Asymptotically Good Algebraic Codes 167

11.1．A Simple Nonconstructive Example 167

11.2．Justesen Codes 168

11.3．Comments 172

11.4．Problems 172

CHAPTER 12 Arithmetic Codes 173

12.1．AN Codes 173

12.2．The Arithmetic and Modular Weight 175

12.3．Mandelbaum-Barrows Codes 179

12.4．Comments 180

12.5．Problems 180

CHAPTER 13 Convolutional Codes 181

13.1．Introduction 181

13.2．Decoding of Convolutional Codes 185

13.3．An Analog of the Gilbert Bound for Some Convolutional Codes 187

13.4．Construction of Convolutional Codes from Cyclic Block Codes 188

13.5．Automorphisms of Convolutional Codes 191

13.6．Comments 193

13.7．Problems 194

Hints and Solutions to Problems 195

References 218

Index 223