Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space

L. Panek, N. M. P. Panek

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.

References


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DOI: https://doi.org/10.5540/tema.2020.021.02.271

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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