  The sum-rank metric can be seen as a generalization of both, the rank and the
Hamming metric. It is well known that sum-rank metric codes outperform rank
metric codes in terms of the required field size to construct maximum distance
separable codes (i.e., the codes achieving the Singleton bound in the
corresponding metric). In this work, we investigate the covering property of
sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend
to answer the question: what is the minimum cardinality of a code given a
sum-rank covering radius? We show the relations of this quantity between
different metrics and provide several lower and upper bounds for sum-rank
metric codes.
