1 citations · 4 across the 7 of their papers we have counts for
7 papers
Decompositions of q-Matroids Using Cyclic Flats
Heide Gluesing-Luerssen, Benjamin Jany
We study the direct sum of q-matroids by way of their cyclic flats. Using that the rank function of a q-matroid is fully determined by the cyclic flats and their ranks, we show tha…
Duality and LP Bounds for Codes with Locality
Anina Gruica, Benjamin Jany, Alberto Ravagnani
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and in…
Representability of the Direct Sum of -Matroids
Heide Gluesing-Luerssen, Benjamin Jany
While there are many parallels between matroid theory and -matroid theory, most notably on the level of cryptomorphisms, there are substantial differences when it comes to the d…
The Projectivization Matroid of a -Matroid
Benjamin Jany
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…
Coproducts in Categories of q-Matroids
Heide Gluesing-Luerssen, Benjamin Jany
q-Matroids form the q-analogue of classical matroids. In this paper we introduce various types of maps between q-matroids. These maps are not necessarily linear, but they map subsp…
Independent Spaces of q-Polymatroids
Heide Gluesing-Luerssen, Benjamin Jany
This paper is devoted to the study of independent spaces of q-polymatroids. With the aid of an auxiliary q-matroid it is shown that the collection of independent spaces satisfies t…
q-Polymatroids and Their Relation to Rank-Metric Codes
Heide Gluesing-Luerssen, Benjamin Jany
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-metri…