ABSTRACT
Let be a poset that is an union of disjoint chains of the same length and be the space of N-tuples over the finite field . Let , with , be a family of finite-dimensional linear spaces such that and let endow with the poset block metric induced by the poset P and the partition , encompassing both Niederreiter-Rosenbloom-Tsfasman metric and error-block metric. In this paper, we give a complete description of group of isometries of the metric space , also called the Niederreiter-Rosenbloom-Tsfasman block space. In particular, we reobtain the group of isometries of the Niederreiter-Rosenbloom-Tsfasman space and obtain the group of isometries of the error-block metric space.
Keywords:
error-block metric; poset metric; Niederreiter-Rosenbloom-Tsfasman metric; ordered Hamming metric; isometries; automorphisms