Sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems. In this paper, we first consider the problem of minimizing the weighted integrated sidelobe level (WISL), which can be used to design sequences with impulse-like autocorrelation and a zero (or low) correlation zone. Two algorithms based on the general majorization-minimization method are developed to tackle the WISL minimization problem with guaranteed convergence to a stationary point. The proposed methods are then extended to optimize the lp-norm of the autocorrelation sidelobes, which leads to a way to minimize the peak sidelobe level (PSL) criterion. All the proposed algorithms can be implemented via the fast Fourier transform (FFT) and thus are computationally efficient. An acceleration scheme is considered to further accelerate the algorithms. Numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller PSL compared with some well known analytical sequences.