On Projective Plane Over A Finite Field of Order Seventeen and its Application to Error-Correcting Codes

Abstract

The aim of the paper is to classify certain geometric structures, called arcs. The main computing tool is the mathematical programming language GAP. In the plane PG(2,17), the important arcs are called complete and are those that cannot be increased to a larger arc. So far, all arcs up to and including size eight have been classified, as have complete 10-arcs, 11-arcs, 12-arcs, 13-arcs and 14-arcs. In the plane of order seventeen, the maximum size is eighteen. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length.