Partial period distribution of FCSR sequences

Klapper and Goresky (1995) introduced feedback with carry shift register (FCSR) and presented a significant kind of FCSR sequences, that is, l-sequences. They showed that the number of 0s and 1s occurring in one of their periods are equal. We discuss the partial period distribution of l-sequences, and show that when the periods become large, the proportion of 1s (resp., 0s) occurring in any of their partial periods approximates 50%.