The independence of two randomness properties of sequences over finite fields

doi:10.1016/j.jco.2011.10.007

Journal of Complexity

Volume 28, Issue 2, April 2012, Pages 154-161

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Abstract

We prove the logical independence of a complexity-theoretic and a statistical randomness property of sequences over a finite field. The two properties relate to the linear complexity profile and to the $\infty$ -distribution of sequences, respectively. The proofs are given by constructing counterexamples to the presumed logical implications between these two properties.

Highlights

► Complexity-theoretic and statistical randomness properties are usually independent. ► A good linear complexity profile need not imply an $\infty$ -distribution. ► An $\infty$ -distribution need not imply a good linear complexity profile.

Keywords

Linear complexity

Random sequence

Stream cipher

Complete uniform distribution