On the maximum imbalance of binary sequences with low aperiodic autocorrelations

Binary sequences with low aperiodic autocorrelation function sidelobes, such as Barker, quasi-Barker, and minimum peak sidelobe sequences have found extensive applications in radar and communications systems. However, there is no systematic method to construct such desirable binary sequences except the use of time consuming and costly exhaustive computer search. In this paper, an upper bound on the maximum imbalance of binary sequences with low aperiodic autocorrelation is derived and is expressed in terms of the sequence length, the window size and the peak sidelobe levels. It sheds some light on the tradeoff between the sequence parameters involved and may be useful in developing efficient sequence searches.