## Function Fields by García and Quoos

In [1], García and Quoos consider global function fields over **F**_{b} given by the Kummer extension of the type

*y*

^{m}= ,

where *m* is a divisor of *b*−1, *f* is a polynomial over **F**_{b} with deg *f* ≥ *b*, and *R*(*f* (*x*)) denotes the reduced polynomial, obtained from *f* (*x*) by operating on its monomials as follows: *R*(*x*^{i}) = *x*^{i} for *i* = 0,…, *b*−1 and *R*(*x*^{i}) = *R*(*x*^{i−(b−1)}) for *i* ≥ *b*.

Based on this definition, formulas for *g*(*F*/**F**_{b}) and *N*(*F*/**F**_{b}) are obtained.

The major part of the paper consists of examples, giving explicit polynomials *f* and integers *m* yielding fields with good parameters.

### References

[1] | Arnaldo García and Luciane Quoos. A construction of curves over finite fields. Acta Arithmetica, 98(2):181–195, 2001. |

### 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. “Function Fields by García and Quoos.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_FGarciaQuoos.html