Csajbók, Bence and Marino, Giuseppe and Polverino, Olga (2018) Classes and equivalence of linear sets in PG(1,q^n). JOURNAL OF COMBINATORIAL THEORY SERIES A (157). pp. 402426. ISSN 00973165

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Abstract
The equivalence problem of GF(q)linear sets of rank n of PG(1,q^n) is investigated, also in terms of the associated variety, projecting configurations,GF(q)linear blocking sets of Rédei type and MRDcodes. We call an GF(q)linear set L_U of rank n in PG(W,Fq^n) = PG(1,q^n) simple if for any ndimensional GF(q)subspace V of W, L_V is PGammaL(2, q^n)equivalent to L_U only when U and V lie on the same orbit of GammaL(2,q^n). We prove that U = {(x,Tr(x)) : x \in GF(q^n)} defines a simple GF(q)linear set for each n. We provide examples of nonsimple linear sets not of pseudoregulus type for n > 4 and we prove that all GF(q)linear sets of rank 4 are simple in PG(1,q^4).
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria 
Depositing User:  Bence Csajbók 
Date Deposited:  13 Sep 2018 06:17 
Last Modified:  30 Jul 2020 23:15 
URI:  http://real.mtak.hu/id/eprint/83771 
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