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 2 (and some over 3). 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

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: 2008-04-04. http://mint.sbg.ac.at/desc_FDrinfeld.html

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