Classes and equivalence of linear sets in PG(1, qn)

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:157

Article

Csajbok, Bence^1,2  Marino, Giuseppe²  Polverino, Olga² 

[1] Eotvos Lorand Univ, ELTE, MTA ELTE Geometr & Algebra Combinator Res Grp, Dept Geometry, Pazmany P Stny 1-C, H-1117 Budapest, Hungary

[2] Univ Campania Luigi Vanvitelli, Dipartimento Matemat & Fis, Viale Lincoln 5, I-81100 Caserta, Italy

关键词: Linearized polynomial;    Linear set;    Blocking set;    MRD-code;   

DOI  :  10.1016/j.jcta.2018.03.007

来源: Elsevier

【 摘 要 】

The equivalence problem of F-q-linear sets of rank n of PG(1, q(n)) is investigated, also in terms of the associated variety, projecting configurations,]Fq-linear blocking sets of Redei type and MRD-codes. We call an F-q-linear set L-U of rank n in PG(W,F-qn) = PG(1, q(n)) simple if for any n-dimensional F-q-subspace V of W, L-v is P Gamma L(2, q(n))-equivalent to L-U only when U and V lie on the same orbit of Gamma L(2, q(n)). We prove that U = {(x,Tr q(n)/q (x)): x is an element of F-qn defines a simple]Fq-linear set for each n. We provide examples of non-simple linear sets not of pseudoregulus type for n > 4 and we prove that all F-q-linear sets of rank 4 are simple in PG(1, q(4)). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free