  We propose a new efficient iterative method for generating random correlated
binary sequences with prescribed correlation function. The method is based on
consecutive linear modulations of initially uncorrelated sequence into a
correlated one. Each step of modulation increases the correlations until the
desired level has been reached. Robustness and efficiency for the proposed
algorithm are tested by generating sequences with inverse power-law
correlations. The substantial increase in the strength of correlation in the
iterative method with respect to the single-step filtering generation is shown
for all studied correlation functions. Our results can be used for design of
disordered superlattices, waveguides, and surfaces with selective transport
properties.
