Maximum Distance Codes in Mat n,s (Zk) with a Non-Hamming Metric and Uniform Distributions

We establish a bound on the minimum distance for codes in Mat _n,s (Z_k) with respect to their ranks and call codes meeting this bound MDR codes. We extend the relationship between codes in Mat _n,s (Z_k) and distributions in the unit cube and use the Chinese Remainder Theorem to construct codes and distributions.