2015/06/29 by Bence Csajbók, Corrado Zanella, Csajbók, Bence +1
Computer Science · Engineering · Mathematics · #51E20 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1506.08875
openalex publication_date 2015/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Scattered linear sets of pseudoregulus type in PG(1,qt) have been defined and investigated in [G. Lunardon, G. Marino, O. Polverino, R. Trombetti: Maximum scattered linear sets of pseudoregulus type and the Segre Variety \cal Sn,n. J. Algebr. Comb. 39 (2014), 807--831.; G. Donati, N. Durante: Scattered linear sets generated by collineations between pencils of lines. J. Algebr. Comb. 40 (2014), 1121-1134]. 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 [G. Lunardon, O. Polverino: Translation ovoids of orthogonal polar spaces. Forum Math. 16 (2004), 663-669], (ii) as a set whose image under the field reduction map is the hypersurface of degree t in PG(2t-1,q) studied in [M. Lavrauw, J. Sheekey, C. Zanella: On embeddings of minimum dimension of PG(n,q)× PG(n,q). Des. Codes Cryptogr. 74 (2015), 427-440], (iii) as exterior splash, by the correspondence described in [M. Lavrauw, J. Sheekey, C. Zanella: On embeddings of minimum dimension of PG(n,q)× PG(n,q). Des. Codes Cryptogr. 74 (2015), 427-440]. In particular, given a canonical subgeometry Σ of PG(t-1,qt), 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.