67 citations · 110 across the 23 of their papers we have counts for
15 papers · 1 filter
Invariants of Tutte Partitions and a -Analogue
Eimear Byrne, Andrew Fulcher
We describe a construction of the Tutte polynomial for both matroids and -matroids based on an appropriate partition of the underlying support lattice into intervals that corres…
Saturating systems and the rank covering radius
Matteo Bonini, Martino Borello, Eimear Byrne
We introduce the concept of a rank saturating system and outline its correspondence to a rank-metric code with a given covering radius. We consider the problem of finding the value…
The Cyclic Flats of a -Matroid
Gianira N. Alfarano, Eimear Byrne
In this paper we develop the theory of cyclic flats of -matroids. We show that the lattice of cyclic flats, together with their ranks, uniquely determines a -matroid and henc…
Weighted Subspace Designs from -Polymatroids
Eimear Byrne, Michela Ceria, Sorina Ionica +1
The Assmus-Mattson theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs. In this work we present a further t…
Constructions of New q-Cryptomorphisms
Eimear Byrne, Michela Ceria, Relinde Jurrius
In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-…
Anticodes in the Sum-Rank Metric
Eimear Byrne, Heide Gluesing-Luerssen, Alberto Ravagnani
We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear…