Rational Function Field

The rational function field F = Fb(x) is an algebraic function field with full constant field Fb and genus g(F/Fb) = 0. It has N(F/Fb) = b + 1 rational places, which can be identified with the b zeros of the linear polynomials and with the pole of x, usually denoted by . The corresponding curve is the projective line PG(1, b), the rational points are P = (1 : 0) and Px = (x : 1) for xFb.

Optimality

Rational function fields meet the upper Hasse-Weil-Bound with equality and are therefore maximal function fields.

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. “Rational Function Field.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_FRational.html

Show usage of this method