A characterization of projective subspaces of codimension two as quasi-symmetric designs with good blocks

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Consider an incidence structure whose points are the points of a PGn (n + 2, q) and whose block are the subspaces of codimension two, where n ≥ 2. Since every two subspaces of codimension two intersect in a subspace of codimension three or codimension four, it is easily seen that this incidence structure is a quasi-symmetric design. The aim of this paper is to prove a characterization of such designs (that are constructed using projective geometries) among the class of all the quasi-symmetric designs with correct parameters and with every block a good block. The paper also improves an earlier result for the special case of n = 2 and obtains a Dembowski-Wagner-type result for the class of all such quasi-symmetric designs. © 2006.

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Discrete Mathematics