Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space

Abstract

Let P = ({1, 2, ..., n}, ≤) be a poset that is an union of disjoint chains of the same length and V = F^N_q be the space of N-tuples over the finite field Fq. Let Vi = F^{k_i}_q , with 1 ≤ i ≤ n, be a family of finite-dimensional linear spaces such that k_1 + k_2 + ... + k_n = N and let V = V_1×V_2×...×V_n endow with the poset block metric d_(P,π) induced by the poset P and the partition π = (k_1, k_2, ..., k_n), 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 (V, d_(P,π)), 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
• symmetries
• isometries.