An $(m,n,R)$-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 $(m,n,R)$-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.

翻译：摘要：一个$(m,n,R)$-德布鲁因覆盖阵列(dBCA)是字母表大小为$q$的双周期$M \times N$阵列，其所有$m \times n$窗口构成的集合形成半径为$R$的覆盖码。通过概率方法给出了$(m,n,R)$-dBCA最小阵列面积的上界，该方法类似于用于德布鲁因覆盖序列长度上界的概率方法。提出了一种从德布鲁因覆盖序列或德布鲁因覆盖序列码构造dBCA的折叠技术。此外，还提供了若干新构造方法，可生成更短的德布鲁因覆盖序列以及面积更小的$(m,n,R)$-dBCA。这些构造主要基于循环码导出的序列、自对偶序列、本原多项式、交织技术、折叠操作以及具有相同覆盖半径序列的互移技术。最后，还讨论了德布鲁因覆盖序列码的构造方法。