Symmetry Group of Ordered Hamming Block Space

Abstract

Let $P=(\{1,2,\dots ,n,\le )$ be a poset that is an union of disjoint chains of the same length and $V={\mathbb{F}}_q^N$ be the space of $N$-tuples over the finite field ${\mathbb{F}}_q$. Let $V_i={\mathbb{F}}_q^{k_i}$, $1\le i\le n$, be a family of finite-dimensional linear spaces such that $k_1+k_2+\dots +k_n=N$ and let $V=V_1\oplus V_2\oplus \dots \oplus V_n$ endow with the poset block metric $d_{(P,\pi )}$ induced by the poset $P$ and the partition $\pi =(k_1,k_2,\dots ,k_n)$, 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 $(V,d_{(P,\pi )})$, called the ordered Hammming block space. In particular, we reobtain the group of symmetries of the Niederreiter-Rosenbloom-Tsfasman space and obtain the group of symmetries of the error-block metric space.