Partial period distribution of FCSR sequences
At Eurocrypt'95, Klapper and Goresky introduced feedback with carry shift register (FCSR) and presented a significant kind of FCSR sequences, that is, I-sequences. They showed that the number of 0's and 1's occurring in one of their periods are equal. Here, we discuss the partial period distribution of I-sequences, and show that when the periods become large, the proportion of 1's (resp., 0's) occurring in any of their partial periods approximates 50%.
partial period distribution feedback with carry shift register (fcsr) l-sequences linear recurring sequence