Symmetry Group of Ordered Hamming Block Space

Let P = ({1, 2, . . . , n,≤) be a poset that is an union of disjoint chains of the same length and V = Fq be the space of N -tuples over the finite field Fq. Let Vi = F ki q , 1 ≤ i ≤ n, be a family of finitedimensional linear spaces such that k1 + k2 + . . . + kn = N and let V = V1⊕V2⊕ . . .⊕Vn endow with the poset block metric d(P,π) induced by the poset P and the partition π = (k1, k2, . . . , kn), encompassing both Niederreiter-Rosenbloom-Tsfasman metric and error-block metric. In this paper, we give a complete description of group of symmetries of the metric space (V, d(P,π)), called the ordered Hammming block space. In particular, we reobtain the group of symmetries of the NiederreiterRosenbloom-Tsfasman space and obtain the group of symmetries of the error-block metric space.