Weighted Subspace Designs from $q$-Polymatroids

Eimear Byrne (1) , Michela Ceria (2) , Sorina Ionica (3) , Relinde Jurrius (4)

1 UCD - University College Dublin [Dublin]
2 Polytechnic University of Bari / Politecnico di Bari
3 MIS - Modélisation, Information et Systèmes - UR UPJV 4290
4 The Netherlands Defence Academy

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 $q$-polymatroid and outline several of its properties.

Domaines: Mathématiques [math]; Informatique [cs]

Eimear Byrne, Michela Ceria, Sorina Ionica, Relinde Jurrius. Weighted Subspace Designs from $q$-Polymatroids. Journal of Combinatorial Theory, Series A, 2024, 201. ⟨hal-03251251⟩