On the Hermitian curve and its intersections with some conics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jul 2014Embargo end date: 01 Feb 2014 Italy English Publisher:Elsevier BVJournal:Finite Fields and Their Applications, volume 28, pages 166-187 (issn: 1071-5797,

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Authors: Chiara Marcolla; Marco Pellegrini 0003; Massimiliano Sala;

doi: 10.1016/j.ffa.2014.02.005 , 10.48550/arxiv.1402.3829

arXiv: 1402.3829

handle: 11572/66922 , 2158/841514

On the Hermitian curve and its intersections with some conics

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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.

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)

Country

Italy

Related Organizations

University of Florence
Italy
University of Trento
Italy

Keywords

intersection, Algebraic coding theory; cryptography (number-theoretic aspects), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Curves over finite and local fields, Hermitian curve, parabola, FOS: Mathematics, Hermitian curve; Intersection; Parabola, Hermitian curve; intersection; parabola

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