Function Fields by García and Quoos
In [1], García and Quoos consider global function fields over Fb given by the Kummer extension of the type
, where m is a divisor of b−1, f is a polynomial over Fb with deg f ≥ b, and R(f (x)) denotes the reduced polynomial, obtained from f (x) by operating on its monomials as follows: R(xi) = xi for i = 0,…, b−1 and R(xi) = R(xi−(b−1)) for i ≥ b.
Based on this definition, formulas for g(F/Fb) and N(F/Fb) 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.”
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Version: 2015-09-03.
http://mint.sbg.ac.at/desc_FGarciaQuoos.html