A linear set view on KM-arcs

In this paper, we study KM-arcs of type t, i.e., point sets of size (q+t) in (mathrm {PG}(2,q)) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular (mathbb {F}_2)-linear set, called an i -club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmáros-Mazzocca, Gács-Weiner and Limbupasiriporn. We show the KM-arcs of type (q/4) recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a family of KM-arcs of type (q/4). We show that this family, apart from new examples that are not translation KM-arcs, contains all translation KM-arcs of type (q/4).