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arXiv · 1402.3829

On the Hermitian curve and its intersections with some conics

Chiara Marcolla·Marco Pellegrini·Massimiliano Sala
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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.

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Chiara Marcolla, Marco Pellegrini, Massimiliano Sala. 2014-02-16. On the Hermitian curve and its intersections with some conics. https://doi.org/10.1016/j.ffa.2014.02.005

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