I. Introduction
Rank metric codes have found various applications in network coding [21], [27], space time coding [15], magnetic recording and cryptography [4], [17], among others. A rank metric code is a collection of matrices over a finite field and the distance between two codewords is defined as the rank of their difference. The concept of rank metric was first introduced by Hua [12], and then considered in coding theory by Delsarte [1]. By adapting the idea of Reed-Solomon codes, Gabidulin [3] gave a construction of a class of rank metric codes which is optimal and achieves the Singleton bound. In [19], Roth gave a construction of a class of maximum rank array codes which is equivalent to Gabidulin’s construction. A rank metric code is said to be decodable up to rank errors if for any codeword can be recovered from whenever has rank at most