  Sequences with low aperiodic autocorrelation sidelobes are well known to have
extensive applications in active sensing and communication systems. In this
paper, we consider the problem of minimizing the weighted integrated sidelobe
level (WISL), which can be used to design sequences with impulse-like
autocorrelation and zero (or low) correlation zone. Two algorithms based on the
general majorization-minimization method are developed to tackle the WISL
minimization problem and the convergence to a stationary point is guaranteed.
In addition, the proposed algorithms can be implemented via fast Fourier
transform (FFT) operations and thus are computationally efficient, and an
acceleration scheme has been considered to further accelerate the algorithms.
Moreover, the proposed methods are extended to optimize the $\ell_{p}$-norm of
the autocorrelation sidelobes, which lead to a way to minimize the peak
sidelobe level (PSL) criterion. 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.
