2019/06/30 by Corrado Zanella, Ferdinando Zullo · 26 citations
Computer Science · Engineering · Mathematics · #Algebraic number #Algorithm #Coding theory and cryptography #Combinatorics #Discrete mathematics #Finite Group Theory Research #Geometry #Graph #Linear subspace #Mathematical analysis #Mathematics #Projection (relational algebra) #Subspace topology #Vertex (graph theory) #graph theory and CDMA systems #math.CO #msc:05B25 #msc:51E20 #msc:51E22
paper · pdf · doi:10.1016/j.disc.2019.111800
published in Discrete Mathematics 343(5), 111800 (Elsevier BV)
openalex created_date 2019/06/27 · openalex publication_date 2020/01/16 · arxiv created 2020/01/18 · arxiv updated 2020/09/25 · openalex updated_date 2026/08/05
In this paper we investigate the geometric properties of the configuration consisting of a k-subspace Γ and a canonical subgeometry Σ in PG(n-1,qn), with Γ∩Σ=∅. The idea motivating is that such properties are reflected in the algebraic structure of the linear set which is projection of Σ from the vertex Γ. In particular we deal with the maximum scattered linear sets of the line PG(1,qn) found by Lunardon and Polverino and recently generalized by Sheekey. Our aim is to characterize this family by means of the properties of the vertex of the projection as done by Csajbók and the first author of this paper for linear sets of pseudoregulus type. With reference to such properties, we construct new examples of scattered linear sets in PG(1,q6), yielding also to new examples of MRD-codes in \mathbb Fq6× 6 with left idealiser isomorphic to \mathbb Fq6.