On the relative abundance of nonbinary sequences with perfect autocorrelations

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. Perfect autocorrelation sequences are however very rare. We recall a technique that yields examples of nonbinary sequences with perfect autocorrelation over enlarged PSK (PSK+) alphabets. It turns out that there are a large number of existing sequence constructions that we can utilize yield perfect correlation sequences, and that this affords a large number of choices for the length and alphabet of such sequences. We have also considered sequences with ideal autocorrelation with respect to their LPI/LPD properties and obtained initial results in this direction.