Linear Complexity of A Family of Binary pq 2 -periodic Sequences From Euler Quotients.

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.