Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places

Acta Arithmetica

Volumn 79, Issue 1, 1997, Pages 59-76

  Niederreiter, Harald ^a   Xing, Chaoping ^b  

^a ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031537194     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-79-1-59-76     Document Type: Article

References (28)

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. _, _, On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory, to appear.
4. D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91.
5. _, Stickelberger elements in function fields, Compositio Math. 55 (1985), 209-239.
6. _, 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.
7. 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.
8. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge University Press, Cambridge, 1994.
9. H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.
10. _, _, Explicit global function fields over the binary field with many rational places, Acta Arith. 75 (1996), 383-396.
11. _, _, Quasirandom points and global function fields, in: Finite Fields and Applications, S. D. Cohen and H. Niederreiter (eds.), Cambridge University Press, Cambridge, 1996, 269-296.
12. M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322.
13. H.-G. Quebbemann, Cyclotomic Goppa codes, IEEE Trans. Inform. Theory 34 (1988), 1317-1320.
14. M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378.
15. 2 with many rational points, J. Number Theory 41 (1992), 6-14.
16. 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.
17. q, Sém. Théorie des Nombres 1982-1983, Exp. 22, Univ. de Bordeaux I, Talence, 1983.
18. _, Résumé des cours de 1983-1984, Annuaire du Collège de France (1984), 79-83.
19. _, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985.
20. H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
21. M. A. Tsfasman and S. G. Vlǎdut, Algebraic-Geometric Codes, Kluwer, Dordrecht, 1991.
22. 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.
23. _, _, How to construct curves over finite fields with many rational points, preprint, 1995.
24. C. Voßand T. Høholdt, A family of Kummer extensions of the Hermitian function field, Comm. Algebra 23 (1995), 1551-1566.
25. C. P. Xing, Multiple Kummer extension and the number of prime divisors of degree one in function fields, J. Pure Appl. Algebra 84 (1993), 85-93.
26. C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102.
27. _, _, Modules de Drinfeld et courbes algébriques ayant beaucoup de points rationnels, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 651-654.
28. _, _, Drinfeld modules of rank 1 and algebraic curves with many rational points, preprint, 1996.