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.
This work was supported by National Key Foundation Research 973 Project (No. G1999035802), National Nature Science Foundation Project (No. 60273027) and National Distinguished Youth Science Foundation Project (No. 60025205) of China.
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Hu, H., Feng, D. (2005). On the 2-Adic Complexity and the k-Error 2-Adic Complexity of Periodic Binary Sequences. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_12
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DOI: https://doi.org/10.1007/11423461_12
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