Codes over Galois rings with respect to the Rosenbloom–Tsfasman metric

We investigate the structure of codes over Galois rings with respect to the Rosenbloom–Tsfasman (shortly RT) metric. We define a standard form generator matrix and show how we can determine the minimum distance of a code by taking advantage of its standard form. We compute the RT-weights of a linear code given with a generator matrix in standard form. We define maximum distance rank (shortly MDR) codes with respect to this metric and give the weights of the codewords of an MDR code. Finally, we give a decoding technique for codes over Galois rings with respect to the RT metric.