On the peak-to-average power ratio of M-sequences

We prove that in the finite field F=FqF=Fq, q=2mq=2m, with a primitive element αα, there exists a nonzero element ββ such thatmaxt∈[0,1)∑k=0q-2(-1)Tr(βαk)e2πikt⩾1π2qlnlnq.As an application of this result we show that the peak-to-average power ratio of the maximal-length shift-register sequences (M-sequences) tends to infinity when their length grows.