On the Hermitian curve and its intersections with some conics
arXiv:1402.3829 · doi:10.1016/j.ffa.2014.02.005
Abstract
We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In particular, we provide explicit counting formulas that have also applications to some Hermitian codes.
This article is contained in previous article "On the Hermitian curve, its intersections with some conics and their applications to affine-variety codes and Hermitian codes" (arXiv:1208.1627)