The Asymptotic Normalized Linear Complexity of Multisequences
Abstract
We show that the asymptotic linear complexity of a multisequence a in Fq∞ that is I := liminf La(n)/n and S := limsup La(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 20 multisequences a. This answers an Open Problem by Dai, Imamura, and Yang. Keywords: Linear complexity, multisequence, Battery Discharge Model, isometry.
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