On the relative abundance of nonbinary sequences with perfect autocorrelations

Abstract

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.

Large low probability of intercept properties of the quaternary sequence with optimal correlation property constructed by legendre sequences

“…The triple correlation properties of maximal length sequences were obtained by Wagner et al [7], and were discussed by the authors [8] who also obtained computational results on the triple autocorrelation of the Legendre and GMW sequences and partial theoretical results of the triple autocorrelation of the Gold sequences. Recently, Boztas and Udaya have proposed the LPI property of various sequences by deriving the triple correlation property [9].…”