The Asymptotic Normalized Linear Complexity of Multisequences

Abstract: We show that the asymptotic linear complexity of a multisequence a in F_q^\infty that is I := liminf L_a(n)/n and S := limsup L_a(n)/n satisfy 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^{\aleph_0} multisequences a. This answers an Open Problem by Dai, Imamura, and Yang. Keywords: Linear complexity, multisequence, Battery Discharge Model, isometry.