Advances in Mathematics of Communications (AMC)

On weighted minihypers in finite projective spaces of square order

Pages: 291 - 309, Volume 9, Issue 3, August 2015      doi:10.3934/amc.2015.9.291

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Linda Beukemann - Technische Hochschule Mittelhessen, Fachbereich MND, Campus Friedberg, Wilhelm-Leuschner-Straße 13, D-61169 Friedberg, Germany (email)
Klaus Metsch - Justus-Liebig-Universität, Mathematisches Institut, Arndtstraβe 2, D-35392 Giessen, Germany (email)
Leo Storme - Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent, Belgium (email)

Abstract: In [11], weighted $\{\delta(q+1),\delta;k-1,q\}$-minihypers, $q$ square, were characterized as a sum of lines and Baer subgeometries $PG(3,\sqrt{q})$ provided $\delta$ is sufficiently small. We extend this result to a new characterization result on weighted $\{\delta v_{\mu+1},\delta v_{\mu};k-1,q\}$-minihypers. We prove that such minihypers are sums of $\mu$-dimensional subspaces and of (projected) $(2\mu+1)$-dimensional Baer subgeometries.

Keywords:  Minihypers, Griesmer bound, Baer subgeometries, blocking sets.
Mathematics Subject Classification:  Primary: 51E20; Secondary: 05B25.

Received: December 2013;      Available Online: July 2015.