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Keywords

Rational Point Finite Field Elliptic Curf Abelian Variety Weierstrass Point 
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Bibliography

  1. BARG A.M., KATSMAN G.L, TSFASMAN M.A. Algebraic geometric codes got from curves of small genus PreprintGoogle Scholar
  2. CARTIER P. Sur la rationalité des diviseurs en Géométrie Algébrique Bull. Soc. Math. France, 177–251 1958Google Scholar
  3. CANTOR D.G. Computing in the Jacobian of a Hyperelliptic Curve Math. of Comp, 48,no177 95–101 1987Google Scholar
  4. CHAO MING LIU, KUMAR P.V. On the maximum length of Goppa codes on elliptic curves Preprint 1987Google Scholar
  5. CHEVALLEY C. Introduction to the theory of algebraic functions of one variable Mathematical Surveys no6, American Mathematical Society 1951Google Scholar
  6. DRIENCOURT Y. Some properties of elliptic codes over a field of characteristic 2 Proc 3rd international conf., AAECC-3, Lect. Notes in Comp Sc. Springer,229 1985Google Scholar
  7. DRIENCOURT Y. Codes elliptiques auto-duaux sur un corps de caractéristique 2 PreprintGoogle Scholar
  8. DRIENCOURT Y.MICHON J.F. Elliptic codes over fields of characteristic 2 Journal of pure and applied algebra 1987Google Scholar
  9. DRIENCOURT Y., MICHON J.F. Remarques sur les codes géométriques C.R. Acad. Sc.Paris, 301 15–17 1985Google Scholar
  10. DRIENCOURT Y., STICHTENOTH J.F. A criterium for self duality of geometric codes Communications in algebra (to appear)Google Scholar
  11. DRINFELD V.G., VLADUT S.G. Number of points of an algebraic curve, Funct. Anal., 17 53–54 1983Google Scholar
  12. FULTON W. Algebraic curves (Benjamin) New-York 1969Google Scholar
  13. GOPPA V.D. Code on algebraic curves Sov. Math Dokl, 24 170–172 1981Google Scholar
  14. GOPPA V.D. Algebraico-geometric codes Math Ussr Izvestiya, vol 21 75–91 1983Google Scholar
  15. GOPPA V.D. Codes and information Russian Math. Surveys, vol 39-1 87–141 1984Google Scholar
  16. GOPPA V.D. Codes associated with divisors Prob. Pered. Inform.Vol 13, No 1, 33–39 1977Google Scholar
  17. HANSEN J.P. Codes on the Klein quartic,ideals and decoding Preprint), Aarhus university 1987Google Scholar
  18. HARTSHORNE R. Algebraic Geometry Graduate Texts in Math., no52, Springer 1977Google Scholar
  19. HASSNER M., BURGE W., WATT S.M. Symbolic computation of Error Control Codes on the Elliptic Riemann Surface Talk in this AAECC-conference 1988Google Scholar
  20. IHARA Y. Some remarks on the number of rational points of algebraic curvesover finite fields J. Fac. Sci. Tokyo,IA 28 721–724 1981Google Scholar
  21. JUSTESEN J., LARSEN K.J., ELBRØND JENSEN H., HAVEMOSE A. and HØHOLDT T. Construction and decoding of a class of algebraic geometry codes The technical University of Denmark, Mat-report no1988-10 1988Google Scholar
  22. KATSMAN G.L., TSFASMAN M.A. Spectra of algebraic geometric codes Prob. Pered. Informa. VOL 23, no4, 19–34 1987Google Scholar
  23. KATSMAN G.L., TSFASMAN M.A., A remark on algebraic geometric codes preprint (to appear in Contemp. Math.) 1987Google Scholar
  24. KATSMAN G.L., TSFASMAN M.A., VLADUT S.G. Modular curves and codes with polynomial complexity of construction Probl. Info. Trans.,20 35–42 1984Google Scholar
  25. KATSMAN G.L., TSFASMAN M.A., VLADUT S.G. Modular curves and codes with polynomial complexity of construction, IEEE Trans., Inf. Theory, 30, No2, 353–355 1984Google Scholar
  26. KRACHKOVSKY V. Yu., A decoding method for algebraic-geometric codes, to appear in the proceedings of the IX-th All Union conference on coding theory and information transmission, Moscow-Odessa 1988Google Scholar
  27. KUMAR P.V., C.M. LIU On the maximum length of MDS Goppa Codes on elliptic curves preprint 1987Google Scholar
  28. LACHAUD G. Les codes géométriques de Goppa Séminaire Bourbaki, no 641 1985Google Scholar
  29. LACHAUD G. Sommes d'Eisenstein et nombre de points de certaines courbes algébriques sur les corps finis Cr. Acad. sci. Paris,305 729–732 1987Google Scholar
  30. LACHAUD G. Codes de Reed et Müller PreprintGoogle Scholar
  31. LANG S. Elliptic functions Addison-Wesley Reading Ma. 1973Google Scholar
  32. LEBRIGAND D., RISLER J.J. Algorithme de Brill-Noether et construction de codes de Goppa Bull. Soc. Math. France (à paraître)Google Scholar
  33. LITSYN S.N., TSFASMAN M.A. Constructive high-dimensional sphere packings Duke Math. Journal, Vol. 54, no 1, 147–161 1987Google Scholar
  34. LITSYN S.N., TSFASMAN M.A. A note on lower bounds PreprintGoogle Scholar
  35. LITSYN S.N., TSFASMAN M.A. Algebraic geometric and number theoric packings of spheres in Rn Uspekhi Math. Nauk.,40 185–186 1985Google Scholar
  36. MAC WILLIAMS F.,SLOANE M.J.A. The theory of error correcting codes North Holland, Amsterdam 1977Google Scholar
  37. LITSYN S.N., TSFASMAN M.A. Construction of dense high dimensional spheres packings Duke Math. J., vol 54, no1 147–161 1987Google Scholar
  38. MAC RAE R.E. On unique factorization in certain rings of algebraic functions J. of algebra,17 243–261 1971Google Scholar
  39. MANIN Y.I. What is the maximum number of points on a curve over F2 J. Fac. Sci. Tokyo, IA 28 715–720 1981Google Scholar
  40. MANIN Y.I., VLADUT S.G. Linear codes and modular curves Soverem. probl. Math. Viniti.,25 209–257 1984Google Scholar
  41. MATZAT H. Ein Vortag über Weierstrasspunkte Thesis Universität Karlsruhe 1975Google Scholar
  42. MICHON J.F. Amélioration des paramètres des codes de Goppa Preprint 1985Google Scholar
  43. MICHON J.F. Les codes BCH comme codes géométriques Preprint 1985Google Scholar
  44. MICHON J.F. Codes de Goppa Sém. Th. Nombres Bordeaux, Exp No7 1983Google Scholar
  45. QUEBBEMANN H.G. Cyclotomic Goppa codes Preprint 1987Google Scholar
  46. QUEBBEMANN H.G. On even codes Preprint 1987Google Scholar
  47. SCHARLAU W. Selbstduale Goppa-Codes Preprint 1987Google Scholar
  48. SCHMIDT F.K. Uber die Erhaltung der Kettensätze der Idealtheorie bei beliebigen endlichen Körpererweiterungen Math Z. 443–450Google Scholar
  49. SCHMIDT F.K. Die Wronskische Determinante in beliebigen differenzierbaren Funktionenkörpern Math. Z. 45, 62–74 1939Google Scholar
  50. SCHMIDT F.K. Zur arithmetischen Theorie der algebraischen Funktionen. II Math. Z. 45, 75–96 1939Google Scholar
  51. SCHMIDT F.K. Zur arithmetischen Theorie der algebraischen Funktionen. I Math. Z. 41 415–438Google Scholar
  52. SCHMIDT F.K. Beweis des Riemann-Rochschen Satzes für algebraische Funftionen mit beliebigen Konstantenkörper Math. Zeit., 41 415–438 1936Google Scholar
  53. SERRE J.P. Sur le nombre des points rationnelś d'une courbe algébrique sur un corps fini Cr. Acad. Sci. Paris,296 397–402 1983Google Scholar
  54. SERRE J.P. Nombre des points des courbes algébruqes sur Fq Sem. Th Nombres Bordeaux Exp. 22 1982–1983Google Scholar
  55. VAN LINT J.H. SPRINGER T.A. Generalized Reed-Solomon codes from Algebraic Geometry IEEE Transactions in Information Theory, Vol IT-33, No 3, 305–309 1987Google Scholar
  56. VLADUT S.G. An exhaustion bound for algebraic — geometric "modular" codes, Probl. Pered. Infor., Vol 23, No1, 28–41 1987Google Scholar
  57. WATERHOUSE W.C. Abelian varieties over finite fields, Ann. Sci. Ec. Norm. Sup.,4ème série, t.2, 521–560 1969Google Scholar
  58. WIRTZ M. On the parameters of Goppa codes Preprint à paraître dans IEEE Information Theory 1987Google Scholar
  59. WOLFMANN J. Nombre de points rationnels de courbes algébriques sur des corps finis associées à des codes cycliques Cr. Acad. Sci. Paris, 305 345–348 1987Google Scholar
  60. ZINOVIEV V.A. Generalized Cascade codes Probl. Info. Trans., 12 2–9 1976Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Jean Francis Michon
    • 1
  1. 1.Département de MathématiquesUniversité Paris 7France

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