Given $[n]=\{ 1,2,\ldots,n\}$, a poset order $\preceq$ on $[n]$, a label map $\pi : [n] \rightarrow \mathbb{ N}$ defined by $\pi(i)=k_i$ with $\sum_{ i=1}^{ n}\pi (i) = N$, and a weight function $w$ on $\mathbb{ F}_{ q}$, let $\mathbb{ F}_{ q}^N$ be the vector space of $N$-tuples over the field $\mathbb{ F}_{ q}$ equipped with $(P,w,\pi)$-metric where $ \mathbb{ F}_q^N $ is the direct sum of spaces $ \mathbb{ F}_{ q}^{ k_1}, \mathbb{ F}_{ q}^{ k_2}, \ldots, \mathbb{ F}_{ q}^{ k_n} $. In this paper, we determine the groups of linear isometries of $(P,w,\pi)$-metric spaces in terms of a semi-direct product, which turns out to be similar to the case of poset (block) metric spaces. In particular, we re-obtain the group of linear isometries of the $(P,w)$-mertic spaces and $(P,\pi)$-mertic spaces.
Categories: math.CO cs.IT math.IT