The geometry of the plan of order seventeen and its application to error-correcting codes

The aim of the thesis is to classify certain geometric structures, called arcs, in a particular setting, namely the projective plane of order seventeen. The main computing tool is the mathematical programming language GAP. First, subsets of the line PG(1; 17) are classiffied. The results on the line PG(1; 17) classify sets of points on the conic on PG(2; 17), since there is a one-to-one correspondence between a set of points on PG(1; 17) and a set of the same size on a conic in PG(2; 17). 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 classiffied, 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. Cubic curves and the related (k; 3)-arcs in PG(2; 17) are also considered. A classiffication of both complete and incomplete curves is determined.