Let p,q be distinct primes with gcd（p-1,q-1） = 4.In this paper,we calculate the autocorrelation values of binary sequences of generalized cyclotomic sets of order four in Z pq and get conditions of p and q such that...Let p,q be distinct primes with gcd（p-1,q-1） = 4.In this paper,we calculate the autocorrelation values of binary sequences of generalized cyclotomic sets of order four in Z pq and get conditions of p and q such that they are four-valued.展开更多
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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 107711001097125011171150)
文摘Let p,q be distinct primes with gcd（p-1,q-1） = 4.In this paper,we calculate the autocorrelation values of binary sequences of generalized cyclotomic sets of order four in Z pq and get conditions of p and q such that they are four-valued.
基金supported by the National Natural Science Foundation of China (Nos.61272492,61103231,61202492,61202395,61462077,and 61562077)the Program for New Century Excellent Talents in University (No.NCET-12-0620)
文摘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.
