Scattered linear sets of pseudoregulus type in 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 L, are proved by means of three different ways to obtain 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) 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), necessary and sufficient conditions are given for the projection of Σ with center a (t-3)-subspace to be a linear set of pseudoregulus type. Furthermore, the q-order sublines are counted and geometrically described.
On scattered linear sets of pseudoregulus type in PG(1,q^t) / Csajbok, B.; Zanella, C.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - STAMPA. - 41:(2016), pp. 34-54. [10.1016/j.ffa.2016.04.006]
On scattered linear sets of pseudoregulus type in PG(1,q^t)
Csajbok B.;
2016-01-01
Abstract
Scattered linear sets of pseudoregulus type in 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 L, are proved by means of three different ways to obtain 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) 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), necessary and sufficient conditions are given for the projection of Σ with center a (t-3)-subspace to be a linear set of pseudoregulus type. Furthermore, the q-order sublines are counted and geometrically described.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
