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.KeywordsPrime NumberBinary SequenceLinear ComplexityStream CipherPeriodic SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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