Affiliation:
1. Departamento de Matemática Universidade Tecnológica Federal do Paraná Pato Branco Paraná Brazil
2. Departamento de Matemática Universidade Estadual de Maringá Maringá Paraná Brazil
3. School of Electrical Engineering and Computer Science University of Ottawa Ottawa Ontario Canada
4. School of Mathematics and Statistics Carleton University Ottawa Ontario Canada
Abstract
AbstractThis work shows several direct and recursive constructions of ordered covering arrays (OCAs) using projection, fusion, column augmentation, derivation, concatenation, and Cartesian product. Upper bounds on covering codes in Niederreiter–Rosenbloom–Tsfasman (shorten by NRT) spaces are also obtained by improving a general upper bound. We explore the connection between ordered covering arrays and covering codes in NRT spaces, which generalize similar results for the Hamming metric. Combining the new upper bounds for covering codes in NRT spaces and ordered covering arrays, we improve upper bounds on covering codes in NRT spaces for larger alphabets. We give tables comparing the new upper bounds for covering codes to existing ones.
Funder
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Natural Sciences and Engineering Research Council of Canada
Subject
Discrete Mathematics and Combinatorics