On linear codes with large weights simultaneously for the Rosenbloom–Tsfasman and Hamming metrics

We show that maximum distance separable (MDS) codes, or more generally nearly MDS codes, for the Rosenbloom–Tsfasman metric can meet the Gilbert–Varshamov bound for their Hamming weights. The proof is based on a careful analysis of orbits of a linear group preserving the Rosenbloom–Tsfasman metric.