On the $N$th $2$-adic complexity of binary sequences identified with algebraic $2$-adic integers

Zhixiong Chen, Arne Winterhof

We identify a binary sequence $\mathcal{S}=(s_n{)}_{n=0}^{\infty }$ with the $2$-adic integer $G_{\mathcal{S}}(2)=\sum _{n=0}^{\infty }{s}_n{2}^n$. In the case that $G_{\mathcal{S}}(2)$ is…