# Introduction to Coding Theory

• J. H. van Lint
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 86)

1. Front Matter
Pages I-XIV
2. J. H. van Lint
Pages 1-21
3. J. H. van Lint
Pages 22-32
4. J. H. van Lint
Pages 33-46
5. J. H. van Lint
Pages 47-63
6. J. H. van Lint
Pages 64-80
7. J. H. van Lint
Pages 81-111
8. J. H. van Lint
Pages 112-127
9. J. H. van Lint
Pages 128-138
10. J. H. van Lint
Pages 139-147
11. J. H. van Lint
Pages 148-166
12. J. H. van Lint
Pages 167-172
13. J. H. van Lint
Pages 173-180
14. J. H. van Lint
Pages 181-194
15. Back Matter
Pages 195-233

### Introduction

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 7l.4• 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 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec­ ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10.

### Keywords

Shannon code coding theory error-correcting code linear optimization

#### Authors and affiliations

• J. H. van Lint
• 1
1. 1.Department of MathematicsEindhoven University of TechnologyEindhovenThe Netherlands

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-58575-3
• Copyright Information Springer-Verlag Berlin Heidelberg 1999
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-63653-0
• Online ISBN 978-3-642-58575-3
• Series Print ISSN 0072-5285
• Buy this book on publisher's site