Some maximal arcs in Hall planes (Q1347005)

The author considers the Thas maximal \(\{q^ 3 - q^ 2 + q; q\}\)-arcs in the desarguesian plane \(PG (2,q)\), with \(q\) even (and \(q\) is always a perfect square). The main result of the paper under review is that for every such maximal arc, one can derive the plane in such a way that the points of the maximal arc not in the derivation set are contained in a maximal \(\{q^ 3 - q^ 2 + q; q\}\)-arc of the derived plane, which is a Hall plane. Hence every Hall plane of even order contains maximal arcs.