Classification of Arcs in Finite Projective Plane of Order Sixteen

Abstract

The aim of this research is to classify certain geometric structures, called arcs. The main computing tool is the Computer algebra system GAP. In the plane PG(2,16), an important arcs are called complete when they can't be increased to a larger arc. So far, all arcs up to size eighteen have been classified. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length.