Vol. 6, No. 1, 2008

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Minimal blocking sets in $\mathsf{PG}(2, q)$ arising from a generalized construction of Megyesi

Nóra V. Harrach and Csaba Mengyán

Vol. 6 (2008), No. 1, 211–226
DOI: 10.2140/iig.2008.6.211
Abstract

We generalize the Megyesi construction for Rédei minimal blocking sets by placing cosets of a multiplicative subgroup of GF(q) {0} on n lines of the affine plane. These points together with the determined directions give a minimal blocking set B with |B| (2 29)q + O(q). We also investigate some constructions in PG(2,qh). We show that if there is a minimal blocking set of size 2q x in PG(2,q), then minimal blocking sets of size 2qh x and 2qh x + 1 exist in PG(2,qh), which are not necessarily of Rédei type.

Keywords
projective plane, blocking set, Rédei type
Mathematical Subject Classification 2000
Primary: 51E21
Milestones
Received: 29 February 2008
Accepted: 9 April 2008
Authors
Nóra V. Harrach
Csaba Mengyán