Ordered Covering Arrays and Upper Bounds on Covering Codes in NRT spaces

This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also obtained by improving a general upper bound. We explore the conn...

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Bibliographic Details
Published inarXiv.org
Main Authors André Guerino Castoldi, Emerson L Monte Carmelo, Moura, Lucia, Panario, Daniel, Stevens, Brett
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.07.2022
Subjects
Arrays
Cartesian coordinates
Upper bounds
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Summary:This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in 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.
ISSN:2331-8422