On the Linear Complexity of a Class of Periodic Sequences Derived from Euler Quotients

In this paper, a family of binary sequences derived from Euler quotients with RSA modulus $pq$ is introduced. Here two primes $p$ and $q$ are distinct and satisfy $\text{gcd}(\pmb{pq},(p-1)(q-1))=1$. The linear complexities and minimal polynomials of the proposed sequences are determined. Besides, this kind of sequences is shown not to have correlation of order four although there exist some special relations by the properties of Euler quotients.