Intersection Numbers For Subspace Designs

Publisher: John Wiley & Sons Inc

E-ISSN: 1520-6610|23|11|463-480

ISSN: 1063-8539

Source: JOURNAL OF COMBINATORIAL DESIGNS, Vol.23, Iss.11, 2015-11, pp. : 463-480

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Abstract

AbstractIntersection numbers for subspace designs are introduced and q‐analogs of the Mendelsohn and Köhler equations are given. As an application, we are able to determine the intersection structure of a putative q‐analog of the Fano plane for any prime power q. It is shown that its existence implies the existence of a 2‐(7,3,q4)q subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed.