An upper bound on the aperiodic autocorrelation function for a maximal-length sequence (Corresp.)

The magnitude of the out-of-phase aperiodic autocorrelation function for a maximal-length linear feedback shift register sequence of period
N
is at most
1 + (2/ \pi)(N + 1)^{1/2} \ln(4N/ \pi)
. Previously, the best upper bound was
(N + 1)^{1/2} \ln (eN)
.