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.
On the Hermitian curve and its intersections with some conics / Marcolla, Chiara; M., Pellegrini; Sala, Massimiliano. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - ELETTRONICO. - 2014, 28:(2014), pp. 166-187. [10.1016/j.ffa.2014.02.005]
On the Hermitian curve and its intersections with some conics
Marcolla, Chiara;Sala, Massimiliano
2014-01-01
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.File in questo prodotto:
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