For classical matroids, the direct sum is one of the most straightforward methods to make a
new matroid out of existing ones. This paper defines a direct sum for q-matroids, the q …

It is well known that linear rank-metric codes give rise to q-polymatroids. Analogously to
matroid theory, one may ask whether a given q-polymatroid is representable by a rank …

We study the direct sum of-matroids by way of their cyclic flats. Using that the rank function of
a-matroid is fully determined by the cyclic flats and their ranks, we show that the cyclic flats of …

There are many similarities between the theories of matroids and $ q $-matroids. However,
when dealing with the direct sum of $ q $-matroids many differences arise. Most notably, it …

In this paper we develop the theory of cyclic flats of q-matroids. We show that the cyclic flats,
together with their ranks, uniquely determine aq-matroid and hence derive a new q …

Abstract 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 paper, we investigate the relation between a-matroid and its associated matroid
called the projectivization matroid. The latter arises by projectivizing the groundspace of the …

While there are many parallels between matroid theory and $ q $-matroid theory, most
notably on the level of cryptomorphisms, there are substantial differences when it comes to …

A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same
size. In this paper we introduce the q-analogue of a PMD and its properties. In order to do …

We describe a construction of the Tutte polynomial for both matroids and q-matroids based
on an appropriate partition of the underlying support lattice into intervals that correspond to …