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Algebraic geometry lattices and codes

  • Michael A. Tsfasman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1122)

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References

  1. [Co/Sl]
    J.H.Conway, N.J.A.Sloane. Sphere packings, lattices and groups. 2nd edition. Springer, N.Y., 1992.Google Scholar
  2. [El]
    N.Elkies. Private communications, 1989–1996.Google Scholar
  3. [Ga/St1]
    A.Garcia, H.Stichtenoth. Algebraic function fields over finite fields with many rational places. In [La/Ts/Ju/We], pp. 1548–1563.Google Scholar
  4. [Ga/St2]
    A.Garcia, H.Stichtenoth. A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vlăduţ bound. Invent.Math., 1995, v. 121, pp. 211–222.Google Scholar
  5. [Go]
    V.D.Gopp. Geometry and codes. Kluwer Acad. Publ., 1988.Google Scholar
  6. [La/Ts]
    G.Lachaud, M.A.Tsfasman. Formules explicites pour les nombre de points des variétés sur un corps fini. Preprint LMD, n.95–25, 1995.Google Scholar
  7. [La/Ts/Ju/We]
    G.Lachaud, M.A.Tsfasman, J.Justesen, V.K.-W.Wei (editors). Special issue on algebraic geometry codes. IEEE Trans. Info. Th., 1995, v.41, n.6, part 1.Google Scholar
  8. [Li/Ts]
    S.N.Litsyn, M.A.Tsfasman. Constructive high-dimensional sphere packings. Duke Math. J., 1987, v. 54, n.1, pp. 147–161.Google Scholar
  9. [Mo]
    C.J.Moreno. Curves over finite fields. Cambridge Univ. Press, 1991.Google Scholar
  10. [Oe]
    J.Oesterlé. Empilements de sphéres. Sém. Bourbaki 727. Astérisque 189–190, 1990, pp. 375–397.Google Scholar
  11. [Pe/Pe/Vl]
    R.Pellikaan, M.Perret, S. Vlăduţ (editors). Arithmetic, geometry and coding theory. Proc. AGCT-4. W.de Gruyter, 1996.Google Scholar
  12. [Qu1]
    H.-G.Quebbemann. Lattices from curves over finite fields. Preprint, 1989.Google Scholar
  13. [Qu2]
    H.-G.Quebbemann. Estimates of regulators and class numbers in function fields. J.Reine Angew.Math., 1991, v. 419, pp. 79–87.Google Scholar
  14. [Ro/Ts1]
    M.Yu.Rosenbloom, M.A.Tsfasman. Multiplicative lattices in global fields. Invent.Math., 1990, v. 101, pp. 687–696.Google Scholar
  15. [Ro/Ts2]
    M.Yu.Rosenbloom, M.A.Tsfasman. Codes for m-metric. Probl. Peredachi Inform. (Probl.Info.Transm.), to appear.Google Scholar
  16. [Se1]
    J.-P.Serre. The number of rational points on curves over finite fields. Princeton lectures. Notes by E.Bayer, 1983.Google Scholar
  17. [Se2]
    J.-P.Serre. Rational points on curves over finite fields. Harvard lectures. Notes by F.Gouvéa, 1985.Google Scholar
  18. [Se3]
    J.-P.Serre. Répartition asymptotique des valeurs propres de l'opérateur de Hecke Tp. Journal AMS, to appear.Google Scholar
  19. [Sh]
    T.Shioda. Mordell-Weil lattices and sphere packings. Amer.J.Math., 1991, v. 113, pp. 931–948.Google Scholar
  20. [Sh/Ts/Vl]
    I.E.Shparlinski, M.A.Tsfasman, S.G. Vlăduţ. Curves with many points and multiplication in finite fields. In [St/Ts], pp. 145–169.Google Scholar
  21. [ST]
    H.Stichtenoth. Algebraic function fields and codes. Springer, 1993.Google Scholar
  22. [St/Ts]
    H.Stichtenoth, M.A.Tsfasman (editors). Coding theory and algebraic geometry. Proc. AGCT-3. Springer Lect. Notes in Math.1518, 1992.Google Scholar
  23. [Tsl]
    M.A.Tsfasman. Global fields, codes and sphere packings. Astérisque 198–200, 1991, pp. 379–396.Google Scholar
  24. [Ts2]
    M.A.Tsfasman. Some remarks on the asymptotic number of points. In [St/Ts], pp. 178–192.Google Scholar
  25. [Ts3]
    M.A.Tsfasman. Algebraic curves and sphere packings. In [Pe/Pe/Vl], pp. 225–251.Google Scholar
  26. [Ts4]
    M.A.Tsfasman. Nombre de points des surfaces sur un corps fini. In [Pe/Pe/Vl], pp. 209–224.Google Scholar
  27. [Ts/Vl1]
    M.A.Tsfasman, S.G. Vlăduţ. Algebraic-geometric codes. Kluwer Acad.Publ., 1991.Google Scholar
  28. [Ts/Vl2]
    M.A.Tsfasman, S.G. Vlăduţ. Geometric approach to higher weights. In [La/Ts/Ju/We], pp. 1564–1588.Google Scholar
  29. [Ts/Vl3]
    M.A.Tsfasman, S.G. Vlăduţ. Asymptotic properties of zeta-functions. Preprint IML, n.96-12, 1996.Google Scholar
  30. [vG/vL]
    J.H.van Lint, G.van der Geer. Linear codes and algebraic curves. Birkhäuser, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Michael A. Tsfasman
    • 1
    • 2
  1. 1.Dobrushin Math. Lab.Institute for Information Transmission ProblemsRussia
  2. 2.Institut des Mathématiques de Luminy du CNRSFrance

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