### The largest size of the arc of degree three in a projective plane of order sixteen

Document Type : Research Paper

Authors

Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

Abstract

An $(n;3)$-arc $K$ in projective plane $PG(2,q)$ of size n and degree three is a set of $n$ points satisfies that every line meets it in less than or equal three points, also it is complete if it is not contained in $(n+1;3)$-arc. The goals of this paper are to construct the projectively inequivalent $(n;3)$-arcs in $PG(2,16)$, determined the largest complete arc in $PG(2,16)$, the stabilizer group of these arcs and we have identified the group with which its isomorph.

Keywords