The asymptotic normalized linear complexity of multisequences

Abstract

We show that the asymptotic linear complexity of a multisequence a ∈ F M q ∞ that is I := lim inf n→∞ L a (n) n and S := lim sup n→∞ L a (n) n satisfies the inequalities M M + 1 S 1 and M(1 − S) I 1 − S M , if all M sequences have nonzero discrepancy infinitely often, and all pairs (I, S) satisfying these conditions are met by 2 ℵ 0 multisequences a. This answers an Open Problem by Dai et al.

Improved results on the probabilistic theory of the joint linear complexity of multisequences

“…An analogous role for word-based stream ciphers is played by the joint linear complexity of multisequences. In recent years, a probabilistic theory of the joint linear complexity of multisequences was developed (see [2][3][4][5][6]). The present paper improves some key results in this theory.…”

Asymptotic analysis on the normalized k-error linear complexity of binary sequences

“…The asymptotic behavior of the normalized linear complexity L n (s)/n for random sequences and multi-sequences was studied in [1], [2] and [14]. The distribution of values of the k-error linear complexity of binary sequences of fixed length was studied by Niederreiter and Paschinger in [11].…”