On two-intersection sets with respect to hyperplanes in projective spaces

[摘要] In [Blokhuis and Lavrauw (Geom. Dedicata 81 (2000), 231-243)] a construction of a class of two-intersection sets with respect to hyperplanes in PG(r - 1, q(t)), rt even, is given, with the same parameters as the union of (q(t/2) - 1)/(q - 1) disjoint Baer subgeometries if t is even and the union of (q(t) - 1)/(q - 1) elements of an (r/2 - 1)-spread in PG(r - 1, q(t)) if t is odd. In this paper, we prove that although they have the same parameters, they are different. This was previously proved in [Ball et at. (Finite Fields Appl. 6 (2000), 294 301)] in the special case where r 3 and t = 4. (C) 2002 Elevier Science (USA).

[发布日期] 2002-08-01