Constructions of de Bruijn sequences from a full-length shift register and an irreducible LFSR

Abstract

In this paper, we study the construction of de Bruijn sequences. A method is given to stretch a de Bruijn sequence of order n to a de Bruijn sequence of order n+k with the help of a k-stage irreducible LFSR. It is shown that there is a correspondence between the cycle structure of an LFSR(l) and that of an NFSR(f⁎l), where f is the characteristic function of a de Bruijn sequence of order n and the LFSR(l) is a k-stage irreducible LFSR. Besides, an efficient algorithm is given to construct a class of de Bruijn sequences whose time complexity is 2n+1O(k) and memory requirement is O(2n+1).