Polynomial Invariants of q-Matroids and Rank-Metric Codes
Abstract
It is shown that the Whitney function of a representable q-matroid and the collection of all higher weight enumerators of any representing rank-metric code determine each other via a monomial substitution. Moreover, the q-matroid itself and the collection of all higher support enumerators of the code determine each other. Next, it is proven that the Whitney function of a q-matroid and the Whitney function of its projectivization determine each other via a monomial substitution. Finally, q-matroids with isomorphic projectivizations are studied. It is shown that the projectivizations are isomorphic iff the q-matroids admit a dimension-preserving lattice isomorphism between their lattices of flats. Such q-matroids are called weakly isomorphic.
Keywords
Cite
@article{arxiv.2509.21618,
title = {Polynomial Invariants of q-Matroids and Rank-Metric Codes},
author = {Heide Gluesing-Luerssen and Benjamin Jany},
journal= {arXiv preprint arXiv:2509.21618},
year = {2025}
}