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Decoding of codes on the klein quartic

  • D. Rotillon
  • J. A. Thiongly
Section 3 Geometric Codes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 514)

Abstract

Following R. Pellikaan who gave, in 1989, an algorithm which decodes geometric codes up to \(t^* = \left[ {\frac{{d^* - 1}}{2}} \right]\) errors where d* is the designed distance of the code, we describe an effective decoding procedure for some geometric codes on the Klein quartic.

Key-words

Geometric codes decoding Jacobian Klein quartic bitangent zeta function 

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References

  1. [1]
    V.D. Goppa. "Geometry and Codes", Mathematics and its applications, soviet Series 24. Kluwer Ac Publ. Dordrecht, The Netherlands, 1989.Google Scholar
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    R. Pellikaan: "On a decoding algorithm for codes on maximal curves". IEEE Trans Inf Theory, Vol. 35, No 6, 1989.Google Scholar
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    A.N. Skorobogatov, S.G. Vladut: "On the decoding of algebraic — Geometric Codes", IEEE Trans Inf Theory, Vol. 36, 5 (Sept. 1990), 1051–1060.CrossRefGoogle Scholar
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    K.O. Stöhr, J.F. Voloch. "A formula for the Cartier operator on plane algebraic curves". J. Reine Angew Math, 377, 49–64, 1987.Google Scholar
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    S.G. Vladut: "On the decoding of algebraic geometric does over F q for q≥16". IEEE Trans Inf Theory, Vol. 36, 6 (Nov. 1990), 1461–1463.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • D. Rotillon
    • 1
    • 3
  • J. A. Thiongly
    • 2
    • 3
  1. 1.University Paul SabatierToulouseFrance
  2. 2.University Toulouse le MirailToulouseFrance
  3. 3.Equipe CNRS 035932 Arithmétique et Théorie de l'Information CIRM Marseille LuminyFrance

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