Cubic arcs in the projective plane over finite field of order four

Abstract

The main aims of this research is to find the stabilizer groups of a cubic curves over a finite field of order 4, also studying the

properties of their groups, and then constructing all different cubic curves, and known which one of them is complete or not. The arcs

of degree 2 which are embedding into a cubic curves of even size have been constructed . Also drawing some of them .