On subcodes of codes in rank metric

Maximum rank distance codes are the equivalent in rank-metric of Reed-Solomon codes whose subcodes have been widely studied. In this paper we characterize subspace subcodes of MRD codes and we show that it is possible to construct efficient polynomial-time encoding-decoding procedures for these subcodes. In a second part we show that subfield subcodes of maximum rank distance codes can be represented in some sense by the direct sum of maximum rank distance codes of smaller length and same minimum distance. We then derive an algorithm correcting some error-patterns beyond the error-correcting capability of the codes