Cubic Arcs in the Projective Plane Over a Finite Field of Order Twenty Three

Abstract

In this research we are interested in finding all the different cubic curves over a finite projective plane of order twenty-three, learning which of them is complete or not, constructing the stabilizer groups of the cubics in, studying the properties of these groups, and, finally, introducing the relation between the subject of coding theory and the projective plane of order twenty three.