The Assmus-Mattson Theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs by Britz et al. in 2009. 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 study the characteristic polynomial of a q-polymatroid and outline several of its properties. We also derive a MacWilliams duality result and apply this to establish criteria on the weight enumerator of a q-polymatroid for which dependent spaces of the q-polymatroid form the blocks of a weighted subspace design.

Assmus-Mattson 定理提供了一种识别由代码产生的块设计的方法。Britz 等人将这一结果扩展到拟阵和加权设计。2009 年。在这项工作中，我们提出了进一步的两重概括：首先是从拟阵到多拟阵，以及从集合到向量空间。为了实现这一目标，我们研究了q多拟阵的特征多项式并概述了它的几个属性。我们还导出了 MacWilliams 对偶结果，并将其应用于建立q多类阵的权重枚举器的标准，其中q多类阵的相关空间形成加权子空间设计的块。