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arXiv · 1512.04818

A linear set view on KM-arcs

Maarten De Boeck·Geertrui Van de Voorde
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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 Korchmaros-Mazzocca, Gacs-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.

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Maarten De Boeck, Geertrui Van de Voorde. 2015-12-15. A linear set view on KM-arcs. https://doi.org/10.1007/s10801-015-0661-7

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