Abstract
An (m, n, R)-\mathbf{de} Bruijn covering array (dBCA) is a doubly periodic M\times N array over an alphabet of size q such that the set of all its m\times n windows form a covering code with radius R . An upper bound of the smallest array area of an (m, n, R)-\mathbf{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)-\mathbf{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.