2024/04/21 by Yeow Meng Chee, Chee, Yeow Meng, Tuvi Etzion +5
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2404.13674
openalex publication_date 2024/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An (m,n,R)-de Bruijn covering array (dBCA) is a doubly periodic M × N array over an alphabet of size q such that the set of all its m × n windows form a covering code with radius R. An upper bound of the smallest array area of an (m,n,R)-dBCA is provided using a probabilistic technique which is similar to the one that was used for an upper bound on the length of a de Bruijn covering sequence. A folding technique to construct a dBCA from a de Bruijn covering sequence or de Bruijn covering sequences code is presented. Several new constructions that yield shorter de Bruijn covering sequences and (m,n,R)-dBCAs with smaller areas are also provided. These constructions are mainly based on sequences derived from cyclic codes, self-dual sequences, primitive polynomials, an interleaving technique, folding, and mutual shifts of sequences with the same covering radius. Finally, constructions of de Bruijn covering sequences codes are also discussed.