Weighted Subspace Designs from -Polymatroids
arXiv:2104.12463
Abstract
The Assmus-Mattson theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs. In this work we present a further two-fold generalisation: first from matroids to polymatroids and also from sets to vector spaces. To achieve this, we introduce the characteristic polynomial of a -polymatroid and outline several of its properties.