Linear isometries on Weighted Coordinates Poset Block Space

11/17/2022

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by   Atul Kumar Shriwastva, et al.

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Given [n]={1,2,…,n}, a poset order ≼ on [n], a label map π : [n] →ℕ defined by π(i)=k_i with ∑_i=1^nπ (i) = N, and a weight function w on 𝔽_q, let 𝔽_q^N be the vector space of N-tuples over the field 𝔽_q equipped with (P,w,π)-metric where 𝔽_q^N is the direct sum of spaces 𝔽_q^k_1, 𝔽_q^k_2, …, 𝔽_q^k_n. In this paper, we determine the groups of linear isometries of (P,w,π)-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,π)-mertic spaces.