On PPM sequences with good autocorrelation properties

The problem of designing sequences of Q-ary pulse-position-modulation (PPM) symbols that have good periodic autocorrelation properties is investigated. Two cases are considered. In the first it is assumed that only slot synchronization is present and thus cyclic shifts are one slot at a time; in the second PPM symbol synchronization is present, in which case cyclic shifts are by one symbol (Q slots) at a time. In both cases, upper bounds are derived on the maximum peak-to-sidelobe distance, which are shown through a computer search to be nearly tight. When symbol synchronization is present, the bound reduces to the Plotkin bound, but it is slightly tighter in general