Skip to main content
SpringerLink
Log in

Amelioration of the McWilliams-Sloane tables using geometric codes from curves with genus 1,2 or 3

  • Coding And Algebraic Geometry
  • Conference paper
  • First Online:
Coding Theory and Applications (Coding Theory 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 311))

Included in the following conference series:

  • 146 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BARG A.M., KATSMAN G.L., TSFASMAN M.A., Algebraic geometric codes got from curves of small genui, preprint.

    Google Scholar 

  2. DRIENCOURT Y., MICHON J.F., Elliptic codes over a field of characteristic 2, à paraître dans le J. of Pure and Applied Algebra.

    Google Scholar 

  3. GOPPA V.D., Algebraico-Geometric Codes, Izv. Akad. Nauk, S.S.S.R. 46 (1982), = Math. U.S.S.R. Izvestiya 21 (1983), 75–91.

    Google Scholar 

  4. GOPPA V.D., Codes and Information, Uspekhi Math. Nauk. 39:1 (1984) 77–120 = Russ. Math. Surveys 39:1 (1984), 87–141.

    Google Scholar 

  5. KATSMAN G.L., TSFASMAN M.A., VLADUT S.G., Modular curves and codes with a polynomial construction, IEEE Trans. Info. Theory 30 (1984), 353–355.

    Google Scholar 

  6. LEBRIGAND D., RISLER J.J., Algorithme de Brill-Noether et codage des codes de Goppa, preprint (Université Paris 6).

    Google Scholar 

  7. LITSYN S.N., TSFASMAN M.A., Algebraic geometric and number theoric packings of spheres in R N, Uspekhi Math. Nauk. 40 (1985) 185–186.

    Google Scholar 

  8. MAC-WILLIAMS F.J., SLOANE N.J.A., The theory of error-correcting codes, North-Holland, Amsterdam 1977.

    Google Scholar 

  9. SERRE J.P., Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C.R. Acad. Sc. Paris 296 (1983) 397–402.

    Google Scholar 

  10. SERRE J.P., Nombre de points des courbes algébriques sur F q , Sém. Th. Nombres Bordeaux (1982–1983) exp.no22.

    Google Scholar 

  11. TSFASMAN M.A., On Goppa codes which are better than the Varshamov-Gilbert bound, Probl. Peredachi Info., 18 (1982), 3–6 = Probl. Info. Trans., 18 (1982), 163–166.

    Google Scholar 

  12. TSFASMAN M.A., VLADUT S.G., ZINK T., Modular curves, Shimura curves and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachrichten 109 (1982), 21–28.

    Google Scholar 

  13. ZINOVIEV V.A., Generalized cascade codes, Probl. Peredachi Info. 12 (1976) 5–15 = Probl. Info. Trans., 12 (1976) 2–9.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Aix-Marseille II & C.I.R.M., France

    Yves Driencourt

  2. Université Paris 7, France

    Jean Francis Michon

Authors
  1. Yves Driencourt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean Francis Michon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

G. Cohen P. Godlewski

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Driencourt, Y., Michon, J.F. (1988). Amelioration of the McWilliams-Sloane tables using geometric codes from curves with genus 1,2 or 3. In: Cohen, G., Godlewski, P. (eds) Coding Theory and Applications. Coding Theory 1986. Lecture Notes in Computer Science, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19368-5_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-19368-5_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19368-5

  • Online ISBN: 978-3-540-39243-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation