An efficient implementation of the D-homomorphism for generation of de Bruijn sequences

An efficient implementation of the D-homomorphism for generating de Bruijn (1946) sequences is presented. The number of exclusive-or operations required to generate the next bit for de Bruijn sequences of order n from a de Bruijn function of order k is shown to be approximately k(2/sup W(n-k)/-1), where W(r) is the number of one's in the binary representation of r: therefore, the number of required operations can be reduced to k if the de Bruijn function is selected appropriately. As an application, the stream cipher is indicated.