Almost perfect sequence family with perfect crosscorrelation

Perfect sequence (PS) is the sequence with zero autocorrelation at all the non-zero phase-shifts and (M, L)almost perfect sequence (APS) is the sequence of period L that has zero autocorrelation except for M non-zero phase-shifts. In this paper, we propose a (q-1/d -1, q
ⁿ
-1/d )-APS family with set size q-/ d -1 constructed from relative difference sets for prime power q and divisor d of q - 1. We further prove that the proposed family has perfect crosscorrelation.