  In this paper we give a randomized reduction for the Rank Syndrome Decoding
problem and Rank Minimum Distance problem for rank codes. Our results are based
on an embedding from linear codes equipped with Hamming distance unto linear
codes over an extension field equipped with the rank metric. We prove that if
both previous problems for rank metric are in ZPP = RP$\cap$coRP, then we would
have NP=ZPP. We also give complexity results for the respective approximation
problems in rank metric.
