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Coding Theory and Algebraic Geometry

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

  • Conference proceedings
  • © 1992

Overview

Editors:
  1. Henning Stichtenoth
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    You can also search for this editor in PubMed   Google Scholar

  2. Michael A. Tsfasman
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    You can also search for this editor in PubMed   Google Scholar

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
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  2. Algebraic geometry and coding theory an introduction

    • Henning Stichtenoth, Michael A. Tsfasman
    Pages 1-3

  3. Reed-Muller codes associated to projective algebraic varieties

    • Yves Aubry
    Pages 4-17

  4. Decoding Algebraic-Geometric Codes by solving a key equation

    • Dirk Ehrhard
    Pages 18-25

  5. On the different of abelian extensions of global fields

    • Gerhard Frey, Marc Perret, Henning Stichtenoth
    Pages 26-32

  6. Goppa codes and Weierstrass gaps

    • Arnaldo Garcia, R. F. Lax
    Pages 33-42

  7. On a characterization of some minihypers in PG(t,q) (q=3 or 4) and its applications to error-correcting codes

    • Noboru Hamada, Tor Helleseth
    Pages 43-62

  8. Deligne-Lusztig varieties and group codes

    • Johan P. Hansen
    Pages 63-81

  9. Spectra of linear codes and error probability of decoding

    • Gregory L. Katsman, Michael A. Tsfasman, Serge G. Vladut
    Pages 82-98

  10. On the true minimum distance of Hermitian codes

    • Kyeongcheol Yang, P. Vijay Kumar
    Pages 99-107

  11. Sphere packings centered at S-units of algebraic tori

    • Boris È. Kunyavskii
    Pages 108-121

  12. A function field related to the Ree group

    • Jens Peter Pedersen
    Pages 122-131

  13. On the gonality of curves, abundant codes and decoding

    • Ruud Pellikaan
    Pages 132-144

  14. Curves with many points and multiplication in finite fileds

    • Igor E. Shparlinski, Michael A. Tsfasman, Serge G. Vladut
    Pages 145-169

  15. The domain of covering codes

    • Philip Stokes
    Pages 170-177

  16. Some remarks on the asymptotic number of points

    • Michael A. Tsfasman
    Pages 178-192

  17. On the weights of trace codes

    • Conny Voss
    Pages 193-198

  18. Minoration de Certaines Sommes Exponentielles Binaires

    • François Rodier
    Pages 199-209

  19. Linear codes, strata of Grassmannians, and the problems of segre

    • Alexei N. Skorobogatov
    Pages 210-223

  20. Back Matter

    Pages 225-228
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Keywords

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.

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, Math. Applications in Chemistry, Computational Intelligence

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