The Asymptotic Normalized Linear Complexity of Multisequences
Information Theory
2007-07-13 v1 Computational Complexity
Cryptography and Security
math.IT
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.
Cite
@article{arxiv.0705.4138,
title = {The Asymptotic Normalized Linear Complexity of Multisequences},
author = {Michael Vielhaber and Monica del Pilar Canales},
journal= {arXiv preprint arXiv:0705.4138},
year = {2007}
}