A note on the cross-correlation function between two binary maximal length linear sequences

Abstract Let { a j }and { a dj } be two binary maximal length linear sequences of period 2 n −1. The cross-correlation function is defined as C d (t) = ∑ j= 0 2n−2 (− 1 ) a j= 1 −a dj for t = 0, 1,…, 2 n − 2. We find the values and the number of occurrences of each value of C d ( t ) when d = 2 n 2 − 2 n 4 + 1 , n ≡ 0 (mod 8).