@article{c156b7a6827a404895e19440fa59479d,
title = "Saturating systems and the rank-metric covering radius",
abstract = "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 of sqm/q(k,ρ) , which is the minimum Fq -dimension of a q-system in Fqmk that is rank- ρ -saturating. This is equivalent to the covering problem in the rank metric. We obtain upper and lower bounds on sqm/q(k,ρ) and evaluate it for certain values of k and ρ . We give constructions of rank- ρ -saturating systems suggested from geometry.",
keywords = "Covering radius, Linear sets, Projective systems, Rank-metric codes, Saturating systems",
author = "Matteo Bonini and Martino Borello and Eimear Byrne",
note = "Funding Information: The results of this paper are the result of a collaboration that arose within the IRC-PHC Ulysses project “Geometric Constructions of Codes for Secret Sharing Schemes.” The research of the first author was partially supported by the Irish Research Council, grant n. GOIPD/2020/597. The second author was partially supported by the ANR-21-CE39-0009 - BARRACUDA (French Agence Nationale de la Recherche). The authors express their deep gratitude to Ferdinando Zullo and Julien Lavauzelle for the inspiring discussions on the subject of the paper. The authors wish to thank the anonymous reviewers for their meticulous reading of this manuscript and whose comments greatly improved this work. Publisher Copyright: {\textcopyright} 2023, The Author(s).",
year = "2023",
month = dec,
doi = "10.1007/s10801-023-01269-9",
language = "English",
volume = "58",
pages = "1173--1202",
journal = "Journal of Algebraic Combinatorics",
issn = "0925-9899",
publisher = "Springer",
number = "4",
}