Post-processing scheme using linear feedback shift registers (LFSRs) for generating chaos-based random bit sequences with infinite period for use in Monte-Carlo methods is discussed. We theoretically analyze auto-correlation functions of choatic binary sequences generated by the Bernoulli chaotic map and a class of binary funcitons. The theoretical analyses can be applied to the LFSR-based post-processing for generating random bit sequences with prescribed auto-correlations because LFSRs can be regarded as a finite bit approximation of the Bernoulli map. Some results of numerical experiments are also given.