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編碼論導論影印版(第3版)

編碼論導論影印版(第3版)

定 價:¥29.00

作 者: J.H.van Lint
出版社: 北京世圖
叢編項: Graduate Texts in Mathematics
標 簽: 暫缺

ISBN: 9787506201162 出版時間: 2003-01-01 包裝: 膠版紙
開本: 24開 頁數(shù): 227 字數(shù):  

內(nèi)容簡介

  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.本書為英文版。

作者簡介

暫缺《編碼論導論影印版(第3版)》作者簡介

圖書目錄

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
 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 Uniformly Packed Codes
 7.5. Nonexistence Theorems
 7.6. Comments
 7.7. Problems
CHAPTER 8 Codes over Z4
 8.1. Quaternary Codes
 8.2. Binary Codes Derived from Codes over Z4
 8.3. Galois Rings over Z4
 8.4. Cyclic Codes over Z4
 8.5. Problems
CHAPTER 9 Ooppa 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

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