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arXiv · 1405.6110

Intersection numbers for subspace designs

Michael Kiermaier·Mario Osvin Pavčević
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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.

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Michael Kiermaier, Mario Osvin Pavčević. 2014-05-23. Intersection numbers for subspace designs. https://doi.org/10.1002/jcd.21403

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