Abstract
The aim of this 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 classified. The results on the line PG(1, 17) classify
sets of points on the conic 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 the 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
classified, as have complete 10-arcs, 11-arcs, 12-arcs, 13-arcs, and 14-arcs. In the plane
of older 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 classification
of both complete and in complete curves is determined.