Drinfeld Modules of Rank 1

Using narrow ray class extensions obtained from Drinfelʹd modules of rank 1, new algebraic function fields can be constructed. These methods are developed in [1], yielding new fields over ℤ₂ (and some over ℤ₃). In [2], similar methods are used for obtaining new fields over F₄ (and one example over F₈). In [3], [2, Theorem 3] is used for constructing fields over F₉ and F₂₇. The methods presented in [4] lead to fields over F₄, F₈, F₉, F₁₆, and F₂₇.

See also

• [5, Section 4.2]

References

[1]	Chaoping Xing and Harald Niederreiter. Drinfeld modules of rank 1 and algebraic curves with many rational points. Monatshefte für Mathematik, 127(3):219–241, April 1999. doi:10.1007/s006050050036 MR1680515 (2000a:11088)
[2]	Harald Niederreiter and Chaoping Xing. Drinfeld modules of rank 1 and algebraic curves with many rational points. II. Acta Arithmetica, 81(1):81–100, 1997. MR1454158 (99d:11064)
[3]	Harald Niederreiter and Chaoping Xing. Nets, (t, s)-sequences, and algebraic geometry. In Peter Hellekalek and Gerhard Larcher, editors, Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics, pages 267–302. Springer-Verlag, 1998.
[4]	Harald Niederreiter and Chaoping Xing. A general method of constructing global function fields with many rational places. In J. P. Buhler, editor, Algorithmic Number Theory, volume 1423 of Lecture Notes in Computer Science, pages 555–566. Springer-Verlag, 1998. doi:10.1007/BFb0054892
[5]	Harald Niederreiter and Chaoping Xing. Rational Points on Curves over Finite Fields: Theory and Applications, volume 285 of Lect. Note Series of the London Math. Soc. Cambridge University Press, 2001. MR1837382 (2002h:11055)

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Drinfeld Modules of Rank 1.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_FDrinfeld.html