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编码论导论 第3版PDF|Epub|txt|kindle电子书版本网盘下载
- J.H.VANLINT著 著
- 出版社： 世界图书出版公司北京公司
- ISBN：750620116X
- 出版时间：2003
- 标注页数：227页
- 文件大小：31MB
- 文件页数：247页
- 主题词：
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图书目录
CHAPTER 1 Mathematical Background1
1.1．Algebra1
1.2．Krawtchouk Polynomials14
1.3．Combinatorial Theory17
1.4．Probability Theory19
CHAPTER 2 Shannon's Theorem22
2.1．Introduction22
2.2．Shannon's Theorem27
2.3．On Coding Gain29
2.4．Comments31
2.5．Problems32
CHAPTER 3 Linear Codes33
3.1．Block Codes33
3.2．Linear Codes35
3.3．Hamming Codes38
3.4．Majority Logic Decoding39
3.5．Weight Enumerators40
3.6．The Lee Metric42
3.7．Comments44
3.8．Problems45
CHAPTER 4 Some Good Codes47
4.1．Hadamard Codes and Generalizations47
4.2．The Binary Golay Code48
4.3．The Ternary Golay Code51
4.4．Constructing Codes from Other Codes51
4.5．Reed-Muller Codes54
4.6．Kerdock Codes60
4.7．Comments61
4.8．Problems62
CHAPTER 5 Bounds on Codes64
5.1．Introduction：The Gilbert Bound64
5.2．Upper Bounds67
5.3．The Linear Programming Bound74
5.4．Comments78
5.5．Problems79
CHAPTER 6 Cyclic Codes81
6.1．Definitions81
6.2．Generator Matrix and Check Polynomial83
6.3．Zeros of a Cyclic Code84
6.4．The Idempotent of a Cyclic Code86
6.5．Other Representations of Cyclic Codes89
6.6．BCH Codes91
6.7．Decoding BCH Codes98
6.8．Reed-Solomon Codes99
6.9．Quadratic Residue Codes103
6.10．Binary Cyclic Codes of Length 2n（n odd）106
6.11．Generalized Reed-Muller Codes108
6.12．Comments110
6.13．Problems111
CHAPTER 7 Perfect Codes and Uniformly Packed Codes112
7.1．Lloyd's Theorem112
7.2．The Characteristic Polynomial of a Code115
7.3．Uniformly Packed Codes118
7.4．Examples of Uniformly Packed Codes120
7.5．Nonexistence Theorems123
7.6．Comments127
7.7．Problems127
CHAPTER 8 Codes over Z4128
8.1．Quaternary Codes128
8.2．Binary Codes Derived from Codes over Z4129
8.3．Galois Rings over Z4132
8.4．Cyclic Codes over Z4136
8.5．Problems138
CHAPTER 9 Goppa Codes139
9.1．Motivation139
9.2．Goppa Codes140
9.3．The Minimum Distance of Goppa Codes142
9.4．Asymptotic Behaviour of Goppa Codes143
9.5．Decoding Goppa Codes144
9.6．Generalized BCH Codes145
9.7．Comments146
9.8．Problems147
CHAPTER 10 Algebraic Geometry Codes148
10.1．Introduction148
10.2．Algebraic Curves149
10.3．Divisors155
10.4．Differentials on a Curve156
10.5．The Riemann-Roch Theorem158
10.6．Codes from Algebraic Curves160
10.7．Some Geometric Codes162
10.8．Improvement of the Gilbert-Varshamov Bound165
10.9．Comments165
10.10．Problems166
CHAPTER 11 Asymptotically Good Algebraic Codes167
11.1．A Simple Nonconstructive Example167
11.2．Justesen Codes168
11.3．Comments172
11.4．Problems172
CHAPTER 12 Arithmetic Codes173
12.1．AN Codes173
12.2．The Arithmetic and Modular Weight175
12.3．Mandelbaum-Barrows Codes179
12.4．Comments180
12.5．Problems180
CHAPTER 13 Convolutional Codes181
13.1．Introduction181
13.2．Decoding of Convolutional Codes185
13.3．An Analog of the Gilbert Bound for Some Convolutional Codes187
13.4．Construction of Convolutional Codes from Cyclic Block Codes188
13.5．Automorphisms of Convolutional Codes191
13.6．Comments193
13.7．Problems194
Hints and Solutions to Problems195
References218
Index223