Advertisement

Self-Dual and Decomposable Geometric Goppa Codes

  • C. Munuera
  • R. Pellikaan
Part of the International Centre for Mechanical Sciences book series (CISM, volume 339)

Abstract

In this paper, a necessary and sufficient criterion for self-duality of geometric Goppa codes is given.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Y. Driencourt and J.F. Michon, Rapport sur les codes géométriques, oct. 1986.Google Scholar
  2. [2]
    Y. Driencourt and J.F. Michon, Remarques sur les codes géométriques, C.R. Acad. Sc. Paris 301 (1985), 15–17.zbMATHMathSciNetGoogle Scholar
  3. [3]
    Y. Driencourt and H. Stichtenoth, A criterion for self-duality of geometric codes, Communications in Algebra 17 (4) (1989), 885–898.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    V.D. Goppa, Codes associated with divisors, Probl. Peredachi Inform. 13(1) (1977), 33–39.Google Scholar
  5. V.D. Goppa, Translation: Probl. Inform. Transmission 13 (1977), 22–26.MathSciNetGoogle Scholar
  6. [5]
    V.D. Goppa, Codes on algebraic curves, Dokl. Akad. Nauk SSSR 259 (1981), 1289–1290.MathSciNetGoogle Scholar
  7. V.D. Goppa, Translation: Soviet Math. Dokl. 24 (1981), 170–172.zbMATHGoogle Scholar
  8. [6]
    V.D. Goppa, Algebraico-geometric codes, Izv. Akad. Nauk SSSR 46 (1982)Google Scholar
  9. V.D. Goppa, Translation: Math. USSR Izvestija 21 (1983), 75–91.CrossRefzbMATHGoogle Scholar
  10. [7]
    V.D. Goppa, Codes and information, Russian Math. Surveys 39 (1984), 87–141.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [8]
    C. Munuera and R. Pellikaan, Equality of geometric Goppa codes and equivalence of divisors, preprint, 1992.Google Scholar
  12. [9]
    H. Stichtenoth, Self-dual Goppa codes, J. Pure Appl. Algebra 55 (1988), 199–211.CrossRefzbMATHMathSciNetGoogle Scholar
  13. [10]
    H. Stichtenoth, The automorphisms of geometric Goppa codes, J. Algebra 130 (1990), 113–121.CrossRefzbMATHMathSciNetGoogle Scholar
  14. [11]
    M. Tsfasman and S. Vladut, Algebraic Geometric Codes, Kluwer Ac. Publ, Dordrecht, 1991.Google Scholar
  15. [12]
    C.-P. Xing, When are two geometric Goppa codes equal ?, IEEE Trans. Information Theory IT-38 (1992), 1140–1142.Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • C. Munuera
    • 1
  • R. Pellikaan
    • 2
  1. 1.University of ValladolidValladolidSpain
  2. 2.Eindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations