Complete arcs in Moulton planes of odd order. (Q2881285)

In this interesting paper, the authors construct a complete \((q^2-1)\)-arc in the Moulton plane of order \(q^2\), with \(q\) an odd prime power. The Moulton plane of order \(q^2\) is up to isomorphism unique. It is coordinatized by a quasifield which is obtained by altering the multiplication of the field \(GF(q^2)\) in a suitable manner. In other words, the affine Moulton plane arises from the Desarguesian plane by preserving the same set of points and by altering a few point-line incidences. Starting from a conic in the Desarguesian plane a \((q^2-1)-\)arc is constructed in the Moulton plane. The completeness of this arc is proved when \(q\geq 5\).