An algorithm for computing minimal bidirectional linear recurrence relations
IEEE Transactions on Information Theory
Expected values for the rational complexity of finite binary sequences
Designs, Codes and Cryptography
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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.