Asymptotic behavior of normalized linear complexity of ultimately non-periodic binary sequences

This paper describes the asymptotic behavior of normalized linear complexity of ultimately nonperiodic binary sequence. The linear complexity of sⁿ, L_s(n), is defined as the length of the shortest linear feedback shift register which generates sⁿ. The research method and results studied in this paper seem to be very useful in characterizing the purely random sequence and distinguishing a key stream generator from a uniformly random sequence.