10 papers
Linear Code Conversion in the Merge Regime: General Bounds and Reed-Muller Constructions
Anina Gruica, Benjamin Jany, Stanislav Kruglik
Erasure codes are a core component of most existing large-scale distributed storage systems, ensuring reliability against node failures. Recent work has shown that adapting code pa…
Counting q-Matroids
Benjamin Jany, Relinde Jurrius, Rudi Pendavingh
-Matroids, a -analogue of classical matroids have attracted a lot of attention over the last decade, yet their enumeration remains largely unexplored. In this paper, we study…
Intersecting Codes and the Connectivity of -Matroids
Fabrizio Conca, Benjamin Jany, Alberto Ravagnani
We investigate the structure of intersecting error-correcting codes, with a particular focus on their connection to matroid theory. We establish properties and bounds for intersect…
Convertible Codes for Data and Device Heterogeneity
Anina Gruica, Benjamin Jany, Stanislav Kruglik
Distributed storage systems must handle both data heterogeneity, arising from non-uniform access demands, and device heterogeneity, caused by time-varying node reliability. In this…
The Star Product of Uniformly Random Codes
Johan Vester Dinesen, Ragnar Freij-Hollanti, Camilla Hollanti +2
We consider the problem of determining the expected dimension of the star product of two uniformly random linear codes that are not necessarily of the same dimension. We use a corr…
Polynomial Invariants of q-Matroids and Rank-Metric Codes
Heide Gluesing-Luerssen, Benjamin Jany
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…
Eigenvalue bounds for the quantum chromatic number of graph powers
Aida Abiad, Benjamin Jany
The quantum chromatic number, a generalization of the chromatic number, was first defined in relation to the non-local quantum coloring game. We generalize the former by defining t…
The Cloud and Flock Polynomials of q-Matroids
Heide Gluesing-Luerssen, Benjamin Jany
We show that the Whitney function of a q-matroid can be determined from the cloud and flock polynomials associated to the cyclic flats. These polynomials capture information about…
-Balanced Codes with the Kendall- Metric
Benjamin Jany, Alberto Ravagnani
We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall- metric. We establish an averaging bound for the cardina…
LRCs: Duality, LP Bounds, and Field Size
Anina Gruica, Benjamin Jany, Alberto Ravagnani
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of wei…