Complex sequences with constant magnitude in the time domain and good aperiodic autocorrelation properties are of fundamental interest due to its applications. Their design typically involves the minimization of a nonlinear function that strives to make equal to zero the correlation coefficients in a region of interest. In this letter, the design of unimodular sequences whose aperiodic autocorrelation and aperiodic complementary autocorrelation vanish for a given set of lags is proposed. The sequences are obtained by minimizing a generalized weighted integrated sidelobe level that depends on their complete second-order characterization. Numerical results show that the proposed sequences are ideally suited to identify strictly linear as well as widely linear systems.