Pseudo-random sequences are used extensively for their high speed and security level and less errors. As a branch, the cyclotomic sequences and the generalized ones are studied widely because of their simple mathemati...Pseudo-random sequences are used extensively for their high speed and security level and less errors. As a branch, the cyclotomic sequences and the generalized ones are studied widely because of their simple mathematical structures and excellent pseudo-random properties. In 1998, Ding and Helleseth introduced a new generalized cyclotomy which includes the classical cyclotomy as a special case. In this paper, based on the generalized cyclotomy, new generalized cyclotomic sequences with order two and length pq are constructed. An equivalent definition of the sequences is deduced so that the autocorrelation values of these sequences can be determined conveniently. The construction contributes to the understanding of the periodic autocorrelation structure of cyclotomically-constructed binary sequences, and the autocorrelation function takes on only a few values.展开更多
Let p and q be two distinct odd primes and let d=(p-1,q-1).In this paper,we construct d-ary generalized two-prime Sidelnikov sequences and study the autocorrelation values and linear complexity.
基金This work is supported by the National Natural Science Foundation of China(Grant No.60473028)The research of the second author is also supported in part by the Natural Science Foundation of Fujian Province of China (Grant No.A0540011)the Science and Technology Foundation of Putian City(Grant No.2005S04).
文摘Pseudo-random sequences are used extensively for their high speed and security level and less errors. As a branch, the cyclotomic sequences and the generalized ones are studied widely because of their simple mathematical structures and excellent pseudo-random properties. In 1998, Ding and Helleseth introduced a new generalized cyclotomy which includes the classical cyclotomy as a special case. In this paper, based on the generalized cyclotomy, new generalized cyclotomic sequences with order two and length pq are constructed. An equivalent definition of the sequences is deduced so that the autocorrelation values of these sequences can be determined conveniently. The construction contributes to the understanding of the periodic autocorrelation structure of cyclotomically-constructed binary sequences, and the autocorrelation function takes on only a few values.
文摘Let p and q be two distinct odd primes and let d=(p-1,q-1).In this paper,we construct d-ary generalized two-prime Sidelnikov sequences and study the autocorrelation values and linear complexity.
