Generalized self-shrinking generator

In this correspondence, we present a simple bit-stream generator. It is a specialization of shrinking generator and a generalization of self-shrinking generator. We call it "generalized self-shrinking generator." The family of such generated sequences has a group structure. The correlation between the sequences is quite good and the sequences themselves are balanced. For each k, 0n-k of the sequences have least periods less than 2^k. No more than 1/4 of the sequences have least periods less than 2^n-1. There are two sequences with least periods of 2. There is no sequence with a least period p such that 2\n\n\t\t