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Global function fields with many rational places over the ternary field

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  • Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
  • Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
Bibliografia
  • [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, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.
  • [6] H. Niederreiter and C. P. Xing, Explicit global function fields over the binary field with many rational places, Acta Arith. 75 (1996), 383-396.
  • [7] 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.
  • [8] 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.
  • [9] 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.
  • [10] H. Niederreiter and C. P. Xing, The algebraic-geometry approach to low-discrepancy sequences, in: Monte Carlo and Quasi-Monte Carlo Methods '96, H. Niederreiter et al. (eds.), Lecture Notes in Statist., Springer, New York, to appear.
  • [11] H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points, in: Proc. Number Theory Conf. (Eger, 1996), de Gruyter, Berlin, to appear.
  • [12] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field, Demonstratio Math., to appear.
  • [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] J.-P. Serre, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985.
  • [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, How to construct curves over finite fields with many points, in: Arithmetic Geometry, F. Catanese (ed.), Cambridge Univ. Press, Cambridge, 1997, 169-189.
  • [19] C. P. Xing, Maximal function fields and function fields with many rational places over finite fields of characteristic 2, preprint, 1997.
  • [20] C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102.
  • [21] 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.
  • [22] C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points, preprint, 1996.
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