A linear set view on KM-arcs
Abstract
In this paper, we study KM-arcs of type t, i.e., point sets of size q+ t in 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 F2-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.
Publication Title
Journal of Algebraic Combinatorics
Recommended Citation
De Boeck, M., & Van de Voorde, G. (2016). A linear set view on KM-arcs. Journal of Algebraic Combinatorics, 44 (1), 131-164. https://doi.org/10.1007/s10801-015-0661-7
