Introduction to Coding Theory

1. Front Matter

   Pages I-XIV

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2. Mathematical Background

   • J. H. van Lint

   Pages 1-21

3. Shannon’s Theorem

   • J. H. van Lint

   Pages 22-32

4. Linear Codes

   • J. H. van Lint

   Pages 33-46

5. Some Good Codes

   • J. H. van Lint

   Pages 47-63

6. Bounds on Codes

   • J. H. van Lint

   Pages 64-80

7. Cyclic Codes

   • J. H. van Lint

   Pages 81-111

8. Perfect Codes and Uniformly Packed Codes

   • J. H. van Lint

   Pages 112-127

9. Codes over ℤ4

   • J. H. van Lint

   Pages 128-138

10. Goppa Codes

    • J. H. van Lint

    Pages 139-147

11. Algebraic Geometry Codes

    • J. H. van Lint

    Pages 148-166

12. Asymptotically Good Algebraic Codes

    • J. H. van Lint

    Pages 167-172

13. Arithmetic Codes

    • J. H. van Lint

    Pages 173-180

14. Convolutional Codes

    • J. H. van Lint

    Pages 181-194

15. Back Matter

    Pages 195-233

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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.

• Shannon
• code
• coding theory
• error-correcting code
• linear optimization
• combinatorics

• Department of Mathematics, Eindhoven University of Technology, Eindhoven, The Netherlands

  J. H. Lint

 

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