Periods Distribution in the Linear Feedback Generalized Registers

Abstract

Linear feedback generalized registers (LFGR) can be employed in several fields as sequences generators. For example they can be used in the cryptologic context of stream ciphering techniques as cellular elements for more complex systems. From this point of view it is important to deal with maximum length sequences. In this paper we study the periods distribution of the states sequences, with the aim of finding the total number of n-linear feedback generalized registers whose period has maximum length.