A generalization of the Giulietti-Korchmaros maximal curve

Abstract

We introduce a family of algebraic curves over $\F_{q^{2n}}$ (for an odd $n$) and show that they are maximal. When $n=3$, our curve coincides with the $\F_{q^6}$-maximal curve that has been found by Giulietti and Korchm\'{a}ros recently. Their curve (i.e., the case $n=3$) is the first example of a maximal curve proven not to be covered by the Hermitian curve.

Available Versions of this Item

• A generalization of the Giulietti-Korchmaros maximal curve. (deposited 15 Feb 2008 11:52) [Currently Displayed]
  • A generalization of the Giulietti-Korchmaros maximal curve. (deposited 14 Jul 2008 10:10)
    • A generalization of the Giulietti-Korchmaros maximal curve. (deposited 26 Jul 2010 16:26)