Constructions Of Quaternary Sequences With Optimal Autocorrelation Magnitude

Pseudorandom sequences with good randomness and the property near to white noise, have been widely used in the CDMA system and cryptographic systems and so on. The pseudorandom sequences applied in these fields are expected to have low out-of-phase autocorrelation for synchronization. Among them, the optimal pseudorandom sequences have attracted a lot of attention. As easy for implementation, the quaternary sequences are preferred, especially the optimal ones.Based on the optimal quaternary sequences with odd periods, the paper proposes the property on a binary sequence pair, like the correlation between the two types of Legend sequences. Using binary sequence pairs with the correlation property and the inverse Gray mapping, two kinds of optimal quaternary sequences with odd periods are constructed. Further, combining them with the interleaved technique, two kinds of optimal quaternary sequences with even periods are proposed, which have the unique property that the real elements1,-1and the imaginal elements i,-i are allocated alternatively. These optimal quaternary sequences constructed in the paper are with new periods or different optimal autocorrelation values, which suggests these optimal ones are new.