On the 2-adic complexity and the k-error 2-adic complexity of periodic binary sequences

Authors:
Honggang Hu;Dengguo Feng
Affiliations:
State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China
Venue:
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Year:
2004

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Abstract

In this paper, we point out a significant difference between the linear complexity and the 2-adic complexity of periodic binary sequences. The concept of the symmetric 2-adic complexity of periodic binary sequences is presented based on this observation. We determine the expected value of the 2-adic complexity and derive a lower bound on the expected value of the symmetric 2-adic complexity of periodic binary sequences. Because the 2-adic complexity of periodic binary sequences is unstable, we present the concepts of the k-error 2-adic complexity and the k-error symmetric 2-adic complexity, and lower bounds on them are also derived.