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1996 | 75 | 4 | 383-396
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
75
Numer
4
Strony
383-396
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-09-19
Twórcy
  • Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
Bibliografia
  • [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 𝔽₂ 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 $𝔽_q$, 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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-aav75i4p383bwm
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