On scattered linear sets of pseudoregulus type in PG(1,q^t)

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• 作者：Bence Csajbó ; k ; ^{csajbok.bence@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Corrado Zanella ^{corrado.zanella@unipd.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：51E20
• 刊名：Finite Fields and Their Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：41
• 期：Complete
• 页码：34-54
• 全文大小：473 K

文摘

Scattered linear sets of pseudoregulus type in 513b035495b" title="Click to view the MathML source">PG(1,q^t)$\mathrm{PG}(1,q^t)$ have been defined and investigated in [19]. The aim of this paper is to continue such an investigation. Properties of a scattered linear set of pseudoregulus type, say 51477a3ff1866de0" title="Click to view the MathML source">L$\mathbb{L}$, are proved by means of three different ways to obtain 51477a3ff1866de0" title="Click to view the MathML source">L$\mathbb{L}$: (i) as projection of a q-order canonical subgeometry [20], (ii) as a point set whose image under the field reduction map is the hypersurface of degree t   in PG(2t−1,q)$\mathrm{PG}(2t-1,q)$ studied in [10], (iii) as exterior splash, by the correspondence described in [15]. In particular, given a canonical subgeometry Σ of PG(t−1,q^t)$\mathrm{PG}(t-1,q^t)$, necessary and sufficient conditions are given for the projection of Σ with center a (t−3)$(t-3)$-subspace to be a linear set of pseudoregulus type. Furthermore, the q-order sublines are counted and geometrically described.