Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space

L. Panek, N. M. P. Panek


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.


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


H. Niederreiter, A combinatorial problem for vector spaces over finite fields, Discrete Mathematics, vol. 96, pp. 221-228, 1991.

R. Brualdi, J. S. Graves, and M. Lawrence, Codes with a poset metric, Discrete Mathematics, vol. 147, pp. 57-72, 2008.

K. Feng, L. Xu, and F. J. Hickernell, Linear error-block codes, Finite Fields and Their Applications, no. 12, pp. 638-652, 2006.

M. M. S. Alves, L. Panek, and M. Firer, Error-block codes and poset metrics, Advances in Mathematics of Communications, vol. 2, pp. 95-111, 2008.

M. Y. Rosenbloom and M. A. Tsfasman, Codes for the m-metric, Probl. Inf. Transm., vol. 33, pp. 45-52, 1997.

W. Park and A. Barg, The ordered hamming metric and ordered symmetric channels, in IEEE Internacional Symposium on Information Theory Proceedings, pp. 2283-2287, IEEE, 2011.

K. Lee, The automorphism group of a linear space with the Rosenbloom-Tsfasman metric, Eur. J. Combin., no. 24, pp. 607-612, 2003.

S. Cho and D. Kim, Automorphism group of crown-weight space, Eur. J. Combin., vol. 1, no. 27, pp. 90-100, 2006.

D. Kim, MacWilliams-type identities for fragment and sphere enumerators, Eur. J. Combin., vol. 28, no. 1, pp. 273-302, 2007.

L. Panek, M. Firer, H. Kim, and J. Hyun, Groups of linear isometries on poset structures, Discrete Mathematics, vol. 308, pp. 4116-4123, 2008.

L. Panek, M. Firer, and M. M. S. Alves, Symmetry groups of Rosenbloom-Tsfasman spaces, Discrete Mathematics, vol. 309, pp. 763-771, 2009.

J. Hyun, A subgroup of the full poset-isometry group, SIAM Journal of Discrete Mathematics, vol. 2, no. 24, pp. 589-599, 2010.


Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:



Desenvolvido por:

Logomarca da Lepidus Tecnologia