On the linear complexity of new generalized cyclotomic binary sequences of order two and period pqr
Longfei Liu, Xiaoyuan Yang, Xiaoni Du, Bin Wei · Tsinghua Science & Technology · 2016
Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd(p−1, q−1)=gcd(p−1, r−1)=gcd(q−1, r−1)=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF(2) is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.