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Article Dans Une Revue Journal of Combinatorial Theory, Series A Année : 2024

Weighted Subspace Designs from q-Polymatroids

Résumé

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.

Dates et versions

hal-04473966 , version 1 (22-02-2024)

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Citer

Eimear Byrne, Michela Ceria, Sorina Ionica, Relinde Jurrius. Weighted Subspace Designs from q-Polymatroids. Journal of Combinatorial Theory, Series A, 2024, 201, pp.105799. ⟨10.1016/j.jcta.2023.105799⟩. ⟨hal-04473966⟩

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