Reversible codes in the Rosenbloom-Tsfasman metric

Reversible codes have a range of wide applications in cryptography, data storage, and communication systems. In this paper, we investigated reversible codes under the Rosenbloom-Tsfasman metric (RT-metric). First, some properties of reversible codes in the RT-metric were described. An essential condition for a reversible code to be a maximum distance separable code (MDS code, in short) in the RT-metric was established. A necessary condition for a binary self-dual code to be reversible was proven and the same was generalized for $q$-ary self-dual reversible codes. Several constructions for reversible RT-metric codes were provided in terms of their generator matrices.