Linear complexity problems of level sequences of Euler quotients and their related binary sequences

Zhihua Niu, Zhixiong Chen, Xiaoni Du

The Euler quotient modulo an odd-prime power $p^r(r>1)$ can be uniquely decomposed as a $p$-adic number of the form $$ \frac{u^{(p-1)p^{r-1}} -1}{p^r}\equiv a_0(u)+a_1(u)p+\ldots+…