Construction of Maximal Arcs and Dual Ovals in Translation Planes

Let π be a translation plane of order qd, q even, with GF(q) a subfield of the kernel and for which the corresponding (d − 1)-spread is symplectic. The corresponding projective plane is denoted by πL, where L is the line at infinity of π. In the first part of the paper we construct a (maximal) {q2d−1 − qd + qd−1;qd−1}-arc of πL; in the second part we construct a dual oval in πL, for which the nucleus is the line at infinity L