Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie

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Project financing:

Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type:

Preprint, postprint, working paper, discussion paper

Keywords:

group divisible designs, q-analogs, scattered subspaces, packing designs, divisible sets, Steiner systems