Symmetry groups of Rosenbloom–Tsfasman spaces

Let F q m ⋅ n be the vector space of m ⋅ n -tuples over a finite field F q and P = { 1 , 2 , … , m ⋅ n } a poset that is the finite union of m disjoint chains of length n . We consider on F q m ⋅ n the poset-metric d P introduced by Rosenbloom and Tsfasman. In this paper, we give a complete description of the symmetry group of the metric space ( V , d P ) .