Perfectly balanced binary sequences with optimal autocorrelation

We have found in our recent work that the coding gain of a coded OFDM system can be maximized if the out-of-phase autocorrelation of the encoding sequence is zero for initial lags. The number of lags with zero autocorrelation depends on the channel length. We are interested in unbiased sequences and consider perfectly balanced binary sequences (BBSs) only. Our main goal in this paper is to obtain BBSs with best possible autocorrelation. We also study the properties of difference sets associated with BBSs and prove the non-existence of BBSs under commonly used difference sets.