Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space

Authors

  • L. Panek Universidade Estadual do Oeste do Paraná - UNIOESTE
  • N. M. P. Panek

DOI:

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

Keywords:

Error-block metric, poset metric, Niederreiter-Rosenbloom-Tsfasman metric, ordered Hamming metric, symmetries, isometries.

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.

Author Biography

L. Panek, Universidade Estadual do Oeste do Paraná - UNIOESTE

Centro de Engenharias e Ciências Exatas - CECE, área de matemática pura.

References

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Published

2020-07-22

How to Cite

Panek, L., & Panek, N. M. P. (2020). Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space. Trends in Computational and Applied Mathematics, 21(2), 271. https://doi.org/10.5540/tema.2020.021.02.271

Issue

Vol. 21 No. 2 (2020)

Section

Original Article

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