ArticleOriginal scientific text

Title

Explicit global function fields over the binary field with many rational places

Authors 1, 2

Affiliations

  1. Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
  2. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

Bibliography

  1. L. Carlitz, A class of polynomials, Trans. Amer. Math. Soc. 43 (1938), 167-182.
  2. A. Garcia and H. Stichtenoth, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound, Invent. Math. 121 (1995), 211-222.
  3. A. Garcia and H. Stichtenoth, On the asymptotic behaviour of some towers of function fields over finite fields, preprint, 1995.
  4. D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91.
  5. Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 721-724.
  6. H. Niederreiter and C. P. Xing, Low-discrepancy sequences obtained from algebraic function fields over finite fields, Acta Arith. 72 (1995), 281-298.
  7. H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl., to appear.
  8. H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: Finite Fields and Applications, S. D. Cohen and H. Niederreiter (eds.), Cambridge University Press, Cambridge, to appear.
  9. M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322.
  10. R. Schoof, Algebraic curves over ₂ with many rational points, J. Number Theory 41 (1992), 6-14.
  11. J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397-402.
  12. J.-P. Serre, Nombres de points des courbes algébriques sur _q, Sém. Théorie des Nombres 1982-1983, Exp. 22, Univ. de Bordeaux I, Talence, 1983.
  13. J.-P. Serre, Résumé des cours de 1983-1984, Annuaire du Collège de France (1984), 79-83.
  14. J.-P. Serre, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985.
  15. J.-P. Serre, personal communication, August 1995.
  16. H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
  17. M. A. Tsfasman and S. G. Vlădut, Algebraic-Geometric Codes, Kluwer, Dordrecht, 1991.
  18. G. van der Geer and M. van der Vlugt, Curves over finite fields of characteristic 2 with many rational points, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 593-597.
  19. E. Weiss, Algebraic Number Theory, McGraw-Hill, New York, 1963.
  20. C. P. Xing, Multiple Kummer extension and the number of prime divisors of degree one in function fields, J. Pure Applied Algebra 84 (1993), 85-93.
  21. C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102.
Pages:
383-396
Main language of publication
English
Received
1995-09-19
Published
1996
Exact and natural sciences