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arXiv · 1804.07388

The minimum size of a linear set

Jan De Beule·Geertrui Van de Voorde
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Abstract

In this paper, we first determine the minimum possible size of an Fq-linear set of rank k in PG(1, q^n). We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an Fq- linear set of rank k in PG(2, q^n). In the case k = n, this confirms a conjecture by Sziklai in [9].

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Jan De Beule, Geertrui Van de Voorde. 2018-04-19. The minimum size of a linear set. https://arxiv.org/abs/1804.07388

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