Global function fields with many rational places over the ternary field

Harald Niederreiter; Chaoping Xing

Acta Arithmetica (1998)

  • Volume: 83, Issue: 1, page 65-86
  • ISSN: 0065-1036

How to cite

top

Harald Niederreiter, and Chaoping Xing. "Global function fields with many rational places over the ternary field." Acta Arithmetica 83.1 (1998): 65-86. <http://eudml.org/doc/207106>.

@article{HaraldNiederreiter1998,
author = {Harald Niederreiter, Chaoping Xing},
journal = {Acta Arithmetica},
language = {eng},
number = {1},
pages = {65-86},
title = {Global function fields with many rational places over the ternary field},
url = {http://eudml.org/doc/207106},
volume = {83},
year = {1998},
}

TY - JOUR
AU - Harald Niederreiter
AU - Chaoping Xing
TI - Global function fields with many rational places over the ternary field
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 1
SP - 65
EP - 86
LA - eng
UR - http://eudml.org/doc/207106
ER -

References

top
  1. [1] A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563. Zbl0863.11040
  2. [2] D. Goss, Basic Structures of Function Field Arithmetic, Springer, Berlin, 1996. Zbl0874.11004
  3. [3] D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91. Zbl0292.12018
  4. [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. Zbl0793.11015
  5. [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. [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. Zbl0877.11065
  7. [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. Zbl0932.11050
  8. [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. Zbl0891.11057
  9. [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. Zbl0886.11033
  10. [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. Zbl0884.11031
  11. [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. Zbl0923.11093
  12. [12] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field, Demonstratio Math., to appear. Zbl0922.11098
  13. [13] H.-G. Quebbemann, Cyclotomic Goppa codes, IEEE Trans. Inform. Theory 34 (1988), 1317-1320. Zbl0665.94014
  14. [14] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378. Zbl0632.12017
  15. [15] J.-P. Serre, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985. 
  16. [16] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993. 
  17. [17] M. A. Tsfasman and S. G. Vlădut, Algebraic-Geometric Codes, Kluwer, Dordrecht, 1991. Zbl0727.94007
  18. [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. Zbl0884.11027
  19. [19] C. P. Xing, Maximal function fields and function fields with many rational places over finite fields of characteristic 2, preprint, 1997. 
  20. [20] C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102. 
  21. [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. [22] C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points, preprint, 1996. Zbl0853.11051

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.