Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
Packing and Covering Properties of Rank Metric Codes
IEEE Transactions on Information Theory
A Rank-Metric Approach to Error Control in Random Network Coding
IEEE Transactions on Information Theory
Construction and covering properties of constant-dimension codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Packing and covering properties of subspace codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Packing and covering properties of subspace codes for error control in random linear network coding
IEEE Transactions on Information Theory
Constant-rank codes and their connection to constant-dimension codes
IEEE Transactions on Information Theory
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In this paper, we investigate geometrical properties of the rank metric space and covering properties of rank metric codes. We first establish an analytical expression for the intersection of two balls with rank radii, and then derive an upper bound on the volume of the union of multiple balls with rank radii. Using these geometrical properties, we derive both upper and lower bounds on the minimum cardinality of a code with a given rank covering radius. The geometrical properties and bounds proposed in this paper are significant to the design, decoding, and performance analysis of rank metric codes.