Title :
On the 2-Adic Complexity and the k-Error 2 -Adic Complexity of Periodic Binary Sequences
Author :
Hu, Honggang ; Feng, Dengguo
Author_Institution :
Chinese Acad. of Sci., Beijing
Abstract :
A significant difference between the linear complexity and the 2-adic complexity of periodic binary sequences is pointed out in this correspondence. Based on this observation, we present the concept of the symmetric 2-adic complexity of periodic binary sequences. The expected value of the 2-adic complexity is determined, and a lower bound on the expected value of the symmetric 2-adic complexity of periodic binary sequences is derived. We study the variance of the 2-adic complexity of periodic binary sequences, and the exact value for it is given. Because the k-adic complexity of periodic binary sequences is unstable, we present the concepts of the kappa-error 2-adic complexity and the k-error symmetric 2-adic complexity, and lower bounds on them are also derived. In particular, we give tighter upper and lower bounds for the minimum k-adic complexity of l-sequences by substituting two symbols within one period.
Keywords :
binary sequences; computational complexity; feedback; shift registers; k-error 2-adic complexity; linear complexity; periodic binary sequences; Application software; Approximation algorithms; Arithmetic; Binary sequences; Feedback; Information security; Laboratories; Random sequences; Research and development; Shift registers; $k$-error $2$-adic complexity; $k$-error symmetric $2$-adic complexity; $l$-sequence; $2$-adic complexity; expected value; periodic binary sequence; symmetric $2$-adic complexity; variance;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.913238
