Johnson type bounds on constant dimension codes
Designs, Codes and Cryptography
Bounds on covering codes with the rank metric
IEEE Communications Letters
On metrics for error correction in network coding
IEEE Transactions on Information Theory
On the Decoder Error Probability of Bounded Rank-Distance Decoders for Maximum RankDistance Codes
IEEE Transactions on Information Theory
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
Rank subcodes in multicomponent network coding
Problems of Information Transmission
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Constant-dimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although CDCs obtained by lifting Gabidulin codes, referred to as KK codes, are nearly optimal. In this paper, we first construct a new class of CDCs based on KK codes, referred to as augmented KK codes, whose cardinalities are greater than previously proposed CDCs. We then propose a low-complexity decoding algorithm for our augmented KK codes using that for KK codes. Our decoding algorithm corrects more errors than a bounded subspace distance decoder by taking advantage of the structure of our augmented KK codes. In the rest of the paper we investigate the covering properties of CDCs. We first derive bounds on the minimum cardinality of a CDC with a given covering radius and then determine the asymptotic behavior of this quantity. Moreover, we show that liftings of rank metric codes have the highest possible covering radius, and hence liftings of rank metric codes are not optimal packing CDCs. Finally, we construct good covering CDCs by permuting liftings of rank metric codes.