A new algorithm for the generation of binary de Bruijn sequences

Abstract

A binary de Bruijn sequence is a binary sequence of length 2 n for which all n-tuple sequences are distinct. One common combinatorial method of approach is to consider a shift register producting many short cycles, e.g., the pure cycling register. These cycles are then joined together to form a full cycle. The same practice is followed in this paper. We propose a new algorithm which joins all the pure cycles of the complementing circulating register (CCR) f(X 1 , X 2 , ..., X n )=X 1 to form a full cycle of 2 n . This algorithm uses about 4n bits of storage and 4n units of time to produce the next cycle bit from the last n bits