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arXiv · 1211.3604

Maximum scattered linear sets of pseudoregulus type and the Segre Variety ${\cal S}_{n,n}$

G. Lunardon·G. Marino·O. Polverino·R. Trombetti
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Abstract

In this paper we study a family of scattered $\F_q$--linear sets of rank $tn$ of the projective space $PG(2n-1,q^t)$ ($n \geq 1$, $t\geq 3$), called of {\it pseudoregulus type}, generalizing results contained in [G. Marino, O. Polverino, R. Trombetti: On ${\mathbb F}_q$--linear sets of $\PG(3,q^3)$ and semifields, {\em J. Combin. Theory Ser. A}, {\bf 114} (2007), 769--788] and in [M. Lavrauw, G. Van de Voorde: Scattered linear sets and pseudoreguli, preprint]. As an application, we characterize, in terms of the associated linear sets, some classical families of semifields: the Generalized Twisted Fields and the 2-dimensional Knuth semifields.

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G. Lunardon, G. Marino, O. Polverino, R. Trombetti. 2012-11-15. Maximum scattered linear sets of pseudoregulus type and the Segre Variety ${\cal S}_{n,n}$. https://arxiv.org/abs/1211.3604

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