Introduction to Coding Theory
β J.H. van Lint
π Library
π
1998
π Springer
π English
β¦ LIBER β¦
π
Introduction to coding theory
β Scribed by Ron Roth
- Publisher
- Cambridge University Press
- Year
- 2006
- Tongue
- English
- Leaves
- 578
- Category
- Library
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β¦ Synopsis
Error-correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems. This book introduces the reader to the theoretical foundations of error-correcting codes, with an emphasis on Reed-Solomon codes and their derivative codes. After reviewing linear codes and finite fields, Ron Roth describes Reed-Solomon codes and various decoding algorithms. Cyclic codes are presented, as are MDS codes, graph codes, and codes in the Lee metric. Concatenated, trellis, and convolutional codes are also discussed in detail
Error-correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems. This book introduces the reader to the theoretical foundations of this subject with the emphasis on the Reed-Solomon codes and their derivatives. Linear codes -- Introduction to finite fields -- Bounds on the parameters of codes -- Reed-Solomon and related codes -- Decoding of Reed-Solomon codes -- Structure of finite fields -- Cyclic codes -- List decoding of Reed-Solomon codes -- Codes in the Lee metric -- MDS codes -- Concatenated codes -- Graph codes -- Trellis and convolutional codes -- Basics in modern algebra
β¦ Table of Contents
Frontmatter......Page 1
Contents......Page 5
Preface......Page 9
1 - Introduction......Page 13
2 - Linear Codes......Page 38
3 - Introduction to Finite Fields......Page 62
4 - Bounds on the Parameters of Codes......Page 105
5 - ReedΓ’β’ο¬Solomon and Related Codes......Page 159
6 - Decoding of ReedΓ’β’ο¬Solomon Codes......Page 195
7 - Structure of Finite Fields......Page 230
8 - Cyclic Codes......Page 254
9 - List Decoding of ReedΓ’β’ο¬Solomon Codes......Page 278
10 - Codes in the Lee Metric......Page 310
11 - MDS Codes......Page 345
12 - Concatenated Codes......Page 377
13 - Graph Codes......Page 407
14 - Trellis and Convolutional Codes......Page 464
Appendix: Basics in Modern Algebra......Page 533
Bibliography......Page 539
List of Symbols......Page 565
Index......Page 571
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Error-correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems. This book introduces the reader to the theoretical foundations of this subject with the emphasis on the Reed-Solomon codes and their d
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The first edition of this book was conceived in 1981 as an alternative to outdated, oversized, or overly specialized textbooks in this area of discrete mathematics-a field that is still growing in importance as the need for mathematicians and computer scientists in industry continues to grow. The bo