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编码论导论
图书信息
出版社: 世界图书出版公司; 第1版 (2003年1月1日)
平装: 227页
开本: 24开
ISBN: 750620116X
条形码: 9787506201162
尺寸: 22.3 x 14.9 x 1 cm
重量: 322 g
内容简介
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 Z4. 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 Z4-codes.
本书为英文版。
目录
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
CHAPTER 1 Mathematical Backblound
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 Temary 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 Codetents
7.3. Uniformly Packed Codes
7.4. Examples of Uniformly Packed Codes
7.5. Nonexistence Theorems
7.6. Comments
7.7. Problems
CHAPTER 8 Codes over ■
8.1. Quaternary Codes
8.2. Binary Codes Derived from Codes over ■
8.3. Galois Rings over ■
8.4. Cyclic Codes over■
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 I0 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
