Download PDF - Global function fields with many rational places over the quinary field. IIAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Global function fields with many rational places over the quinary field. II

Authors 1, 2

Affiliations

  1. Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
  2. Department of Information Systems and Computer Science, The National University of Singapore, Lower Kent Ridge Road, Singapore 119260

Bibliography

  1. A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563.
  2. D. Goss, Basic Structures of Function Field Arithmetic, Springer, Berlin, 1996.
  3. D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91.
  4. D. R. Hayes, A brief introduction to Drinfeld modules, in: The Arithmetic of Function Fields, D. Goss, D. R. Hayes, and M. I. Rosen (eds.), de Gruyter, Berlin, 1992, 1-32.
  5. H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: Finite Fields and Applications, S. Cohen and H. Niederreiter (eds.), Cambridge Univ. Press, Cambridge, 1996, 269-296.
  6. H. Niederreiter and C. P. Xing, Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places, Acta Arith. 79 (1997), 59-76.
  7. H. Niederreiter and C. P. Xing, Drinfeld modules of rank 1 and algebraic curves with many rational points. II, Acta Arith. 81 (1997), 81-100.
  8. H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field, Demonstratio Math. 30 (1997), 919-930.
  9. H. Niederreiter and C. P. Xing, The algebraic-geometry approach to low-discrepancy sequences, in: Monte Carlo and Quasi-Monte Carlo Methods 1996, H. Niederreiter et al. (eds.), Lecture Notes in Statist. 127, Springer, New York, 1998, 139-160.
  10. H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points, in: Number Theory, K. Győry, A. Pethő, and V. T. Sós (eds.), de Gruyter, Berlin, 1998, 423-443.
  11. H. Niederreiter and C. P. Xing, Global function fields with many rational places and their applications, in: Proc. Finite Fields Conf. (Waterloo, 1997), Contemp. Math., Amer. Math. Soc., Providence, to appear.
  12. H. Niederreiter and C. P. Xing, Nets, (t,s)-sequences, and algebraic geometry, in: Pseudo- and Quasi- Random Point Sets, P. Hellekalek and G. Larcher (eds.), Lecture Notes in Statist., Springer, New York, to appear.
  13. O. Pretzel, Codes and Algebraic Curves, Oxford Univ. Press, Oxford, 1998.
  14. M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378.
  15. 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.
  16. H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
  17. G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in: Arithmetic Geometry, F. Catanese (ed.), Cambridge Univ. Press, Cambridge, 1997, 169-189.
  18. C. P. Xing and H. Niederreiter, Modules de Drinfeld et courbes algébriques ayant beaucoup de points rationnels, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 651-654.
  19. C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points, Monatsh. Math., to appear.
Acta Arithmetica
1998/86/3
Export to PBN, Opens in new tab
Pages:
277-288
Main language of publication
English
Received
1998-06-22
Published
1998
Exact and natural sciences