We first introduce a family of binary $pq^2$-periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q-1$. The minimal polynomials and linear complexities are determined for the proposed sequences provided that $2^{q-1} \not\equiv 1 \mod{q^2}.$ The results show that the proposed sequences have high linear complexities.

翻译：我们首先推出一个二进制的双进制($pq $2)序列,其依据是Euler 商数模型(modulo $pq $),其中美元和美元是两个截然不同的奇数质,美元是1美元。对于拟议的序列,将确定最小的多元和线性复杂性,条件是$2 q-1}\ not\equiv 1\mod{q%2}。结果显示,拟议的序列具有很高的线性复杂性。