Peak Sidelobe Level and Peak Crosscorrelation of Golay–Rudin–Shapiro Sequences

Sequences with low aperiodic autocorrelation and crosscorrelation are used in communications remote sensing. Golay Shapiro independently devised a recursive construction that produces families of complementary pairs binary sequences. In the simplest case, Rudin–Shapiro sequences, general it what we call Golay–Rudin–Shapiro Calculations by Littlewood show sequences have mean square autocorrelation. A sequence’s peak sidelobe level is its largest magnitude over all nonzero shifts. Høholdt, Jensen, Justesen showed there some undetermined positive constant $A$ such sequence length notation="LaTeX">$2^{n}$ bounded above notation="LaTeX">$A(1.842626\ldots)^{n}$ , where notation="LaTeX">$1.842626\ldots $ real root notation="LaTeX">$X^{4}-3 X-6$ . We notation="LaTeX">$5(1.658967\ldots)^{n-4}$ notation="LaTeX">$1.658967\ldots notation="LaTeX">$X^{3}+X^{2}-2 X-4$ Any exponential bound lower base will fail to be true for almost notation="LaTeX">$n$ any same but prefactor at least one provide similar on (largest shifts) between each pair. The methods use generalize produced recursion, which obtain bounds growth rate as original