DERIVED AND RESIDUAL SUBSPACE DESIGNS

作者：Kiermaier Michael^*; Laue Reinhard

来源：Advances in Mathematics of Communications, 2015, 9(1): 105-115.

DOI：10.3934/amc.2015.9.105

• q-analog
• combinatorial design
• subspace design
• derived design
• residual design
• large set

A generalization of forming derived and residual designs from t-designs to subspace designs is proposed. A q-analog of a theorem by Tran Van Trung, van Leijenhorst and Driessen is proven, stating that if for some (not necessarily realizable) parameter set the derived and residual parameter set are realizable, the same is true for the reduced parameter set.
As a result, we get the existence of several previously unknown subspace designs. Some consequences are derived for the existence of large sets of subspace designs. Furthermore, it is shown that there is no q-analog of the large Witt design.

• 出版日期2015-2