Browsing by Author / Creator "Kiermaier, Michael"

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    Original Data of Publication "q-analogs of group divisible designs"
    (University of Bayreuth, 2018-07-27) Buratti, Marco; Kiermaier, Michael; Kurz, Sascha; Nakic, Anamari; Wassermann, Manfred
    A well known class of objects in combinatorial design theory are group divisible designs. Here, we introduce the q-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces, q-Steiner systems, packing designs and q^r-divisible projective sets. We give necessary conditions for the existence of q-analogs of group divisible designs, construct an infinite series of examples, and provide further existence results with the help of a computer search. One example is a (6,3,2,2)_2 group divisible design over GF(2) which is a packing design consisting of 180 blocks that such every 2-dimensional subspace in GF(2^6) is covered at most twice.