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

Authors:
Idan Alrod;Simon Litsyn;Alexander Yudin
Affiliations:
Department of Electrical Engineering - Systems, Tel Aviv University, Tel Aviv 69978, Israel;Department of Electrical Engineering - Systems, Tel Aviv University, Tel Aviv 69978, Israel;Department of Mathematics, Vladimir State Pedagogical University, Stroiteley 11, Vladimir 600024, Russian Federation
Venue:
Finite Fields and Their Applications
Year:
2006

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Abstract

We prove that in the finite field F=F"q, q=2^m, with a primitive element @a, there exists a nonzero element @b such thatmaxt@?[0,1)@?k=0q-2(-1)^T^r^(^@b^@a^^^k^)e^2^@p^i^k^t=1@p2qlnlnq.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.