Recent results on coding and algebraic geometry

  • J. Wolfmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 229)


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.


Algebraic Geometry Elliptic Curf Linear Code Algebraic Curve Algebraic Curf 
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  1. [1]
    DRIENCOURT. Y, MICHON, J.F. “Remarques sur les codes géométriques” CRAS t. 301, Série 1, no1, (7 Juin 1985)Google Scholar
  2. [2]
    DRIENCOURT. Y, MICHON, J.F. “Elliptic codes over a field of characteristic 2” to appear in JOURNAL OF PURE AND APPLIED ALGEBRAICGoogle Scholar
  3. [3]
    FULTON. W, “Algebraic Curves” BENJAMIN (1969)Google Scholar
  4. [4]
    GOPPA, V.D, “Codes on algebraic curves” SOVIET MATH. DOKL 24 (1981) 170–172Google Scholar
  5. [5]
    GOPPA. V.D, “Codes and Information” RUSSIAN MATH. SURVEYS 39: 1 (1984)Google Scholar
  6. [6]
    KATSMAN. G.L, TSFASMAN. M.A., VLADUT. S.G. “Modular curves and codes with a polynomial construction” IEEE TRANS INF. THEORY. 30 (1984) 353–355Google Scholar
  7. [7]
    LACHAUD. G, “Les codes géométriques de GOPPA” SEM. BOURBAKI, exp. No 641 (1985)Google Scholar
  8. [8]
    Mc ELIECE. R.J, “The theory of information and coding” ENCYCLOPEDIA OF MATH. AND ITS APPL. 3, ADDISON-WESLEY (1977)Google Scholar
  9. [9]
    Mac WILLIAMS. F.J., SLOANE. N.J.A. “The theory of error correcting codes” NORTH-HOLLAND, AMSTERDAM (1977)Google Scholar
  10. [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. [11]
    TATE. J, “The arithmetic of elliptic curves” INVENT. MATH 23 (1974) 179–206Google Scholar
  12. [12]
    TSFASMAN. M.A, VLADUT. S.G, ZINK. T. “Modular curves, Shimura curves and Goppa codes, better Varshamov-Gilbert bound” MATH. NACHR. 109 (1982) 21–28Google Scholar
  13. [13]
    WALKER. R.J, “Algebraic curves” PRINCETON UNIV. PRESS (1950)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • J. Wolfmann
    • 1
  1. 1.GECT, Université de ToulonLa GardeFrance

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