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Introduction to Coding Theory

  • Textbook
  • © 1999

Overview

Authors:
  1. J. H. Lint

    1. Department of Mathematics, Eindhoven University of Technology, Eindhoven, The Netherlands

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

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Table of contents (13 chapters)

  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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Keywords

About this book

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.

Authors and Affiliations

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

    J. H. Lint

About the author

 

Bibliographic Information

  • Book Title: Introduction to Coding Theory

  • Authors: J. H. Lint

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-58575-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Hardcover ISBN: 978-3-540-64133-9Published: 15 December 1998

  • Softcover ISBN: 978-3-642-63653-0Published: 14 October 2012

  • eBook ISBN: 978-3-642-58575-3Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 3

  • Number of Pages: XIV, 234

  • Topics: Combinatorics, Algebraic Geometry, Number Theory

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