The geometry of covering codes in the sum-rank metric
Matteo Bonini, Martino Borello, Eimear Byrne
TL;DR
This paper explores the geometric properties of covering codes in the sum-rank metric, introducing saturating systems and establishing bounds and constructions based on geometric structures.
Contribution
It introduces sum-rank saturating systems, links them to covering properties, and provides bounds and geometric constructions for these systems.
Findings
Established bounds on shortest sum-rank saturating systems.
Connected saturating systems to geometric structures.
Provided new constructions for saturating systems.
Abstract
We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank--saturating systems of a fixed dimension, which is equivalent to the covering problem in the sum-rank metric. We obtain upper and lower bounds on this quantity. We also give constructions of saturating systems arising from geometrical structures.
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