On the 2-Adic Complexity of Cyclotomic Binary Sequences with Period $$p^2$$ and $$2p^2$$

Let p be a prime. In this paper, we obtain the 2-adic complexity of all almost balanced cyclotomic binary sequence of order two with period $$p^2$$ ; and also show the 2-adic complexity of several non-trivial balanced cyclotomic binary sequences of order two with period $$2p^2$$ .