Ordered covering arrays and upper bounds on covering codes. Issue 6 (30th March 2023)

• Record Type: Journal Article
• Authors: Castoldi, André Guerino; Monte Carmelo, Emerson L.; Moura, Lucia; Panario, Daniel; Stevens, Brett
• Is Part Of: Journal of combinatorial designs. Volume 31:Issue 6(2023)
• Page Start: 304
• Page End: 329
• Publication Date: 2023-03-30
• Subjects: bounds on codes -- covering array -- covering code -- Niederreiter–Rosenbloom–Tsfasman metric -- ordered covering array -- ordered orthogonal array; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21882
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: This 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.