An upper bound on the aperiodic autocorrelation function for a maximal-length sequence

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) .