On the distinctness of maximal length sequences over Z/(pq) modulo 2

This paper studies the distinctness problem of the reductions modulo 2 of maximal length sequences over Z/(pq), where p and q are two different odd primes with p1, it is proved that if there exist a nonnegative integer S and a primitive element ξ in Z/(pq) such that , and either (q−1) is not divisible by (p−1) or 2(p−1) divides (q−1), then if and only if . The existence of S and ξ is completely determined by p, q and degf(x). Secondly, for the case of degf(x)=1, it is proved that if gcd(p−1,q−1)=2 and (p−1)/ordp(2) is congruent to (q−1)/ordq(2) modulo 2, then if and only if .