## Innovations in Incidence Geometry

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

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323261

Digital Object Identifier
doi:10.2140/iig.2005.2.35

Mathematical Reviews number (MathSciNet)
MR2214713

Zentralblatt MATH identifier
1103.51006

#### Citation

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. https://projecteuclid.org/euclid.iig/1551323261

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