Ternary sequences with perfect periodic autocorrelation

We construct 0, \pm 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.