The merit factor of Legendre sequences

Turyn has shown by numerical computation that the merit factor of long Legendre sequences offset by a quarter of their length has in all likelihood the asymptotic value 6 . The ergodicity postulate is used in this correspondence to calculate that the merit factor F of a Legendre sequence offset by a fraction f of its length has an asymptotic value given by 1/F=(2/3)-4|f|+8f^{2}, |f|\leq 1/2 , which gives F=6 for |f|=1/4 .