On the structure and decoding of linear codes with respect to the Rosenbloom-Tsfasman metric

We investigate the structure of linear codes over finite fields with respect to recently introduced the Rosenbloom-Tsfasman metric. Given the generator of a linear code in a special triangular form called standard form we give a formula for the spectra of the code. We give a formula for the number of linear codes with a particular length, dimension and the minimum distance with respect to the Rosenbloom-Tsfasman metric. Finally, we propose a decoding technique with respect to this new metric.