A de Bruijn array code is a set of $r \times s$ binary doubly-periodic arrays such that each binary $n \times m$ matrix is contained exactly once as a window in one of the arrays. Such a set of arrays can be viewed as a two-dimensional generalization of a perfect factor in the de Bruijn graph. Necessary conditions for the existence of such codes are given. Several direct constructions and recursive constructions for such arrays are given. A framework for a theory of two-dimensional feedback shift registers which is akin to (one-dimensional) feedback shift registers is suggested in the process.

翻译：德布鲁因阵列码是一组 $r \times s$ 的二元双周期阵列，使得每个二元 $n \times m$ 矩阵恰好作为某个阵列中的一个窗口出现一次。这样的阵列集合可视为德布鲁因图中完美因子在二维上的推广。本文给出了此类码存在的必要条件。提出了几种用于构造此类阵列的直接构造法与递归构造法。在此过程中，提出了一个类似于（一维）反馈移位寄存器的二维反馈移位寄存器理论框架。