Vol. 2, No. 1, 2005

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

Giovanna Bonoli and Olga Polverino

Vol. 2 (2005), No. 1, 35–56
DOI: 10.2140/iig.2005.2.35

An Fq-linear blocking set B of π = PG(2,qn), q = ph, n > 2, can be obtained as the projection of a canonical subgeometry Σ PG(n,q) of Σ = PG(n,qn) to π from an (n 3)-dimensional subspace Λ of Σ, disjoint from Σ, and in this case we write B = BΛ,Σ. In this paper we prove that two Fq-linear blocking sets, BΛ,Σ and BΛ,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 Fq-linear blocking sets of the plane PG(2,q4).

blocking set, canonical subgeometry, linear set
Mathematical Subject Classification 2000
Primary: 05B25, 51E21
Received: 24 January 2005
Accepted: 20 October 2005
Giovanna Bonoli
Olga Polverino