Groups of linear isometries on poset structures

Let V be an n  -dimensional vector space over a finite field FqFq and P={1,2,…,n}P={1,2,…,n} a poset. We consider on V   the poset-metric dPdP. In this paper, we give a complete description of groups of linear isometries of the metric space (V,dP)(V,dP), for any poset-metric dPdP.