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

ym = $\displaystyle {\frac{{f(x)}}{{R(f(x))}}}$,

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.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_FGarciaQuoos.html

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