Bounds on Minimum Rank Distances of Array Codes

Various bounds on minimum rank distances of linear block codes have been proposed. In this paper, we derive a Singleton bound on minimum rank distances of m-by-n array codes. Our Singleton bound not only applies to nonlinear codes, but also implies several previously proposed bounds as special cases. In addition, we derive one upper bound and one lower bound on the size of array codes which parallel the sphere-packing bound and the Gilbert bound. Finally, we propose a construction that leads to maximum rank distance codes that do not require large fields as their alphabets.