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Multi-Covering Radius for Rank Metric Codes

The results of this paper are concerned with the multi-covering radius, a generalization of covering radius, of Rank Distance (RD) codes. This leads to greater understanding of RD codes and their distance properties. Results on multi-covering radii of RD codes under various constructions are given by varying the parameters. Some bounds are established. A relationship between multi-covering radii of an RD code and that of its ambient space is also found. The classical sphere bound is generalized.