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  • Conference proceedings
  • © 1992

Coding Theory and Algebraic Geometry

Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1518)

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Table of contents (18 papers)

  1. Front Matter

    Pages I-VIII
  2. Algebraic geometry and coding theory an introduction

    • Henning Stichtenoth, Michael A. Tsfasman
    Pages 1-3
  3. On the different of abelian extensions of global fields

    • Gerhard Frey, Marc Perret, Henning Stichtenoth
    Pages 26-32
  4. Goppa codes and Weierstrass gaps

    • Arnaldo Garcia, R. F. Lax
    Pages 33-42
  5. Deligne-Lusztig varieties and group codes

    • Johan P. Hansen
    Pages 63-81
  6. Spectra of linear codes and error probability of decoding

    • Gregory L. Katsman, Michael A. Tsfasman, Serge G. Vladut
    Pages 82-98
  7. On the true minimum distance of Hermitian codes

    • Kyeongcheol Yang, P. Vijay Kumar
    Pages 99-107
  8. Sphere packings centered at S-units of algebraic tori

    • Boris È. Kunyavskii
    Pages 108-121
  9. A function field related to the Ree group

    • Jens Peter Pedersen
    Pages 122-131
  10. Curves with many points and multiplication in finite fileds

    • Igor E. Shparlinski, Michael A. Tsfasman, Serge G. Vladut
    Pages 145-169
  11. The domain of covering codes

    • Philip Stokes
    Pages 170-177
  12. Some remarks on the asymptotic number of points

    • Michael A. Tsfasman
    Pages 178-192
  13. On the weights of trace codes

    • Conny Voss
    Pages 193-198
  14. Back Matter

    Pages 225-228

About this book

About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting "Algebraic Geometry and Coding Theory" was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.

Keywords

  • Extension
  • algebraic varieties
  • coding theory
  • error-correcting code
  • finite field

Bibliographic Information

  • Book Title: Coding Theory and Algebraic Geometry

  • Book Subtitle: Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991

  • Editors: Henning Stichtenoth, Michael A. Tsfasman

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0087986

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Softcover ISBN: 978-3-540-55651-0Published: 05 August 1992

  • eBook ISBN: 978-3-540-47267-4Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 232

  • Topics: Algebraic Geometry, Number Theory, Mathematical Applications in Chemistry, Computational Intelligence

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions