Fan, C. T. (HK-HNKG) AMS Author Profile; Fan, S. M. (HK-HNKG) AMS Author Profile; Ma, S. L. (HK-HNKG) AMS Author Profile; Siu, M. K. (HK-HNKG) AMS Author Profile
Source
Ars Combinatoria (Ars Combin.) (19850101), 19, A, 205-213. ISSN: 0381-7032 (print).
Subject
05 Combinatorics -- 05B Designs and configurations 05B15 Orthogonal arrays, Latin squares, Room squares
A de Bruijn sequence of span $n$ is a periodic binary sequence of length $2^n$ in which each subsequence of length $n$ appears exactly once. Here an $(r,s;m,n)$-de Bruijn array is defined to be a periodic $r\times s$ binary array, where $m\le r$, $n\le s$ and $rs=2^{mn}$, in which each of the different $m\times n$ binary matrices appears exactly once. The authors prove that for any $m$ and $n$ there exist $r$ and $s$ such that an $(r,s;m,n)$-de Bruijn array exists, and they offer some methods for constructing these arrays. The case where only nonzero $m\times n$ matrices are considered has been studied by several authors [see, e.g., \n F. J. MacWilliams\en and \n N. J. A. Sloane\en, Proc. IEEE {\bf 64} (1976), no. 12, 1715--1729; MR0439402 (55 \#12295)].