Bounds on MLDR Codes Over ${\mathbb{Z}}_{p^t}$

Upper bounds on the minimum Lee distance of codes that are linear over ${\mathbb{Z}}_q$, $q=p^t$, $p$ prime are discussed. The bounds are Singleton like, depending on the length, rank, and alphabet size of the code. Codes meeting such bounds are referred to as Maximum Lee Distance with respect to Rank (MLDR) Codes. We present some new bounds on MLDR codes, using combinatorial arguments. In the context of MLDR codes, our work provides improvements over existing bounds in the literature