Innovations in Incidence Geometry

$\mathbb{F}_q$-linear blocking sets in $\mathrm{PG}(2,q^4)$

Giovanna Bonoli and Olga Polverino

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An F q -linear blocking set B of π = PG ( 2 , q n ) , q = p h , n > 2 , can be obtained as the projection of a canonical subgeometry Σ PG ( n , q ) of Σ = PG ( n , q n ) to π from an ( n 3 ) -dimensional subspace Λ of Σ , disjoint from Σ , and in this case we write B = B Λ , Σ . In this paper we prove that two F q -linear blocking sets, B Λ , Σ and B Λ , Σ , of exponent h are isomorphic if and only if there exists a collineation φ of Σ mapping Λ to Λ and Σ to Σ . This result allows us to obtain a classification theorem for F q -linear blocking sets of the plane PG ( 2 , q 4 ) .

Article information

Innov. Incidence Geom., Volume 2, Number 1 (2005), 35-56.

Received: 24 January 2005
Accepted: 20 October 2005
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05B25: Finite geometries [See also 51D20, 51Exx] 51E21: Blocking sets, ovals, k-arcs

blocking set canonical subgeometry linear set


Bonoli, Giovanna; Polverino, Olga. $\mathbb{F}_q$-linear blocking sets in $\mathrm{PG}(2,q^4)$. Innov. Incidence Geom. 2 (2005), no. 1, 35--56. doi:10.2140/iig.2005.2.35.

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