In this paper, we present a new iterative algorithm for designing binary sequences with good properties in terms of aperiodic autocorrelation function. The algorithm has a low complexity, growing linearly with the sequence length, and allows improvements with respect to best known sequences, especially for large lengths. First, we show its application to the design of long markers for frame synchronization. In particular, new markers with length 128 and 192 bits are generated and evaluated, showing consistent improvements with respect to current markers used by CCSDS Recommendation for turbo code synchronization at very low SNR. Then, the proposed technique is applied to the design of binary arrays with small values of peak side lobes, as required by various communication and signal processing applications, including radar.