Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen

Authors

Emad Bakr Al-Zangana, Department of Mathematics, College of Science, Al-Mustansiriyah UniversityFollow

Abstract

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

Keywords

Finite geometry, Coding Theory, Elliptic cubic curve, Arc, Inflexion

Article Type

Article

How to Cite this Article

Al-Zangana, Emad Bakr (2016) "Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen," Baghdad Science Journal: Vol. 13: Iss. 4, Article 22.
DOI: https://doi.org/10.21123/bsj.2016.13.4.0846