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We construct 0, 1 sequences of length (q^2l+1-l) / (q-1), where q=2^s, with out-of-phase periodic autocorrelation 0, and in-phase correlation q^2l; SUch that the peak factor of radiation is (q^2l+1-1) / (q^2+l-q^2l), which is close to 1 as q becomes large.
Høholdt et al. (Fri,) studied this question.