Some inherited maximal arcs in derived dual translation planes
Let \(\pi\) be a finite projective plane of order \(q\). A \(\{k;n\}\)-arc \({\mathcal K}\) is a set of \(k\) points such that each line of \(\pi\) meets \({\mathcal K}\) in at most \(n\) points and \(n\) is minimal with that property. \({\mathcal K}\) is called a maximal arc if \(k = q(n - 1) + n\) or equivalently every line meets \({\mathcal K}\) in 0 or \(n\) points. \textit{J. A. Thas} [Geom. Dedicata 3, 61-64 (1974; Zbl 0285.50018)] constructed a class of maximal \(\{q^3 - q^2 + q; q\}\)-arcs in certain translation planes of even order \(q^2\). The duals of these translation planes are derivable and the author shows that the Thas maximal arcs also yield maximal arcs in the derived dual translation planes.
scientific article; zbMATH DE number 806226
scientific article