Skip to main content

Recent results on coding and algebraic geometry

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 229))

Abstract

Construction of GOPPA geometric codes from algebraic curves and some results on these codes improving VARCHAMOV-GILBERT bound are presented. We consider also the particular case of elliptic algebraic curves.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DRIENCOURT. Y, MICHON, J.F. “Remarques sur les codes géométriques” CRAS t. 301, Série 1, no1, (7 Juin 1985)

    Google Scholar 

  2. DRIENCOURT. Y, MICHON, J.F. “Elliptic codes over a field of characteristic 2” to appear in JOURNAL OF PURE AND APPLIED ALGEBRAIC

    Google Scholar 

  3. FULTON. W, “Algebraic Curves” BENJAMIN (1969)

    Google Scholar 

  4. GOPPA, V.D, “Codes on algebraic curves” SOVIET MATH. DOKL 24 (1981) 170–172

    Google Scholar 

  5. GOPPA. V.D, “Codes and Information” RUSSIAN MATH. SURVEYS 39: 1 (1984)

    Google Scholar 

  6. KATSMAN. G.L, TSFASMAN. M.A., VLADUT. S.G. “Modular curves and codes with a polynomial construction” IEEE TRANS INF. THEORY. 30 (1984) 353–355

    Google Scholar 

  7. LACHAUD. G, “Les codes géométriques de GOPPA” SEM. BOURBAKI, exp. No 641 (1985)

    Google Scholar 

  8. Mc ELIECE. R.J, “The theory of information and coding” ENCYCLOPEDIA OF MATH. AND ITS APPL. 3, ADDISON-WESLEY (1977)

    Google Scholar 

  9. Mac WILLIAMS. F.J., SLOANE. N.J.A. “The theory of error correcting codes” NORTH-HOLLAND, AMSTERDAM (1977)

    Google Scholar 

  10. MANIN. Y, “What is the maximum number of points on a curve over IF2” J. FAC. SCI. UNIV. TOKYO. IA 28 (1981) 715–720.

    Google Scholar 

  11. TATE. J, “The arithmetic of elliptic curves” INVENT. MATH 23 (1974) 179–206

    Google Scholar 

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

    Google Scholar 

  13. WALKER. R.J, “Algebraic curves” PRINCETON UNIV. PRESS (1950)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacques Calmet

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wolfmann, J. (1986). Recent results on coding and algebraic geometry. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_720

Download citation

  • DOI: https://doi.org/10.1007/3-540-16776-5_720

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16776-1

  • Online ISBN: 978-3-540-39855-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics