CORRELATION PROPERTIES OF DE BRUIJN SEQUENCES

Several new bounds for the correlation functions of de Bruijn sequences are derived.It is shown that the set of all primitive de Bruijn sequences have the following two properties:1)for each sequence a in the set with large span n,the magnitude of its auto-correlation funct-ion|r(k)|is relatively small compared with the peak 2~n for all k≠0 mod 2~n;2)for each pair of sequences a,b in the set with large span n,the magnitude of their cross-correlation function |r(k)| is relatively small compared with the peak 2~n for all k.Some generalizations of the result are also presented.