Intersection numbers for subspace designs

Titelangaben

Kiermaier, Michael ; Pavčević, Mario Osvin:
Intersection numbers for subspace designs.
In: Journal of Combinatorial Designs. Bd. 23 (2015) Heft 11 . - S. 463-480.
ISSN 1520-6610
DOI: https://doi.org/10.1002/jcd.21403

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Abstract

Intersection 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,q^4)_q subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed.