Constructing de Bruijn sequences by concatenating smaller universal cycles

Abstract

We present sufficient conditions for when an ordering of universal cycles α1,α2,…,αm for disjoint sets S1,S2,…,Sm can be concatenated together to obtain a universal cycle for S=S1∪S2∪⋯∪Sm. When S is the set of all k-ary strings of length n, the result of such a successful construction is a de Bruijn sequence. Our conditions are applied to generalize two previously known de Bruijn sequence constructions and then they are applied to develop three new de Bruijn sequence constructions.