On Two-Intersection Sets with Respect to Hyperplanes in Projective Spaces

Aart Blokhuis, Michel Lavrauw
2002 Journal of combinatorial theory. Series A  
In [Blokhuis and Lavrauw (Geom. Dedicata 81 (2000), 231-243)] a construction of a class of two-intersection sets with respect to hyperplanes in PGðr À 1; q t Þ; rt even, is given, with the same parameters as the union of ðq t=2 À 1Þ=ðq À 1Þ disjoint Baer subgeometries if t is even and the union of ðq t À 1Þ=ðq À 1Þ elements of an ðr=2 À 1Þ-spread in PGðr À 1; q t Þ if t is odd. In this paper, we prove that although they have the same parameters, they are different. This was previously proved in
more » ... [Ball et al. (Finite Fields Appl. 6 (2000), 294-301)] in the special case where r ¼ 3 and t ¼ 4: # 2002 Elsevier Science (USA)
doi:10.1006/jcta.2002.3289 fatcat:durmbtgmynelvgpv32mqkzxziu