The geometry of covering codes in the sum-rank metric
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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