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MacWilliams Identities for q-Polymatroids and Applications

Time Thursday 27 January, 2022 at 15:15 - 16:00
Place Zoom

Abstract: A q-polymatroid consists of a lattice of subspaces of a vector space endowed with a rank function that is both increasing and submodular. They were introduced independently by Gorla et al (2020) and Shiromoto (2019) as q-analogues of polymatroids and in reference to matrix codes. A number of invariants of codes are in fact matroid invariants, including the MacWilliams duality theorem. MacWilliams identities for classical matroids have been studied by a number of authors (e.g. Brylawski, Oxley, Britz, Shiromoto).  In this talk we will consider duality of q-polymatroids and will give a version of a MacWilliams theorem for q-polymatroids, using the characteristic polynomial. As as application of this result, we will state an Assmus-Mattson-like theorem that establishes criteria for the existence of weighted subspace designs arising from a q-polymatroid. This talk is based on joint work with Michela Ceria, Relinde Jurrius, and Sorina Ionica.

To receive the Zoom link, please contact: Klara Stokes

Event type: Seminar

Speaker: Eimear Byrne, University College of Dublin (UCD), Ireland

Klara Stokes
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