Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie
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Project financing:
Deutsche Forschungsgemeinschaft
Abstract
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, design packings 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 design packing consisting of 180 blocks that such every 2-dimensional subspace in GF(2)⁶ is covered at most twice.
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Item Type:
Preprint, postprint
Additional notes (visible to public):
typos corrected
Keywords:
group divisible designs; q-analogs; scattered subspaces; packing designs; divisible sets; Steiner systems