We investigate the covering problem in RT spaces induced by the Rosenbloom-Tsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen and Honkala, Brualdi et al., Yildiz et al. A new construction of MDS codes in RT spaces is obtained. Upper bounds are given on the basis of MDS codes, generalizing well-known results due to Stanton et al., Blokhuis and Lam, and Carnielli. Tables of lower and upper bounds are presented too.
1
Universidade Estadual de Maringá,
Departamento de Matemática,
Maringá, PR
2
Universidade Estadual de Maringá,
Departamento de Matemática,
Maringá, PR
@article{10_37236_4974,
author = {Andr\'e G. Castoldi and Emerson L. Monte Carmelo},
title = {The covering problem in {Rosenbloom-Tsfasman} spaces},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/4974},
zbl = {1358.94104},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4974/}
}
TY - JOUR
AU - André G. Castoldi
AU - Emerson L. Monte Carmelo
TI - The covering problem in Rosenbloom-Tsfasman spaces
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/4974/
DO - 10.37236/4974
ID - 10_37236_4974
ER -
%0 Journal Article
%A André G. Castoldi
%A Emerson L. Monte Carmelo
%T The covering problem in Rosenbloom-Tsfasman spaces
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/4974/
%R 10.37236/4974
%F 10_37236_4974
André G. Castoldi; Emerson L. Monte Carmelo. The covering problem in Rosenbloom-Tsfasman spaces. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/4974
