Autocorrelation Values of the Third Class of the Generalized Cyclotomic Sequences of Order Six ?
نویسندگان
چکیده
Binary sequences which have low autocorrelation values have important applications in communication systems and cryptography. In this paper, the autocorrelation values of the third class binary Whiteman generalized cyclotomic sequences of order six and period pq are discussed completely. Our result shows that the autocorrelation of these sequences is four-valued and that the corresponding values are in {−1, 3, −5, pq} if the parameters are chosen carefully.
منابع مشابه
Autocorrelation Values of Generalized Cyclotomic Sequences of Order Six
The generalized cyclotomic sequence of order two has several good randomness properties and behaves like the Legendre sequence in several aspects. In this correspondence we calculate the autocorrelation values of the generalized cyclotomic sequence of order two. Our result shows that this sequence could have very good autocorrelation property and pattern distributions of length two if the two p...
متن کاملCyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6
Abstract. BinaryWhiteman’s cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman’s generalized cyclotomic sequence (WGCS-I) of order d = 6. Our results show that the autocorrelation values of this sequence is four-valued or five-valued if (n1−1)(n2−1)/36...
متن کاملCyclic code from the first class Whiteman's generalized cyclotomic sequence with order 4
Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular, Ding deduced the exact formulas for the autocorrelation and the linear complexity of these sequences of order 2. In this paper, we consider the generalized sequences of order 4. Under certain conditions, the linear complexity of these sequences...
متن کاملAutocorrelation of New Generalized Cyclotomic Sequences of Period pn
Let n ≥ 2 be a positive integer and Z× n be the multiplicative group of the integer ring Zn. For a partition {Di|i = 0, 1, · · · , d − 1} of Z× n , if there exist elements g1, · · · , gd of Z× n satisfying Di = giD0 for all i where D0 is a multiplicative subgroup of Z× n , the Di are called generalized cyclotomic classes of order d. There have been lots of studies about cyclotomy with respect t...
متن کاملThe linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length 2p
In this article, we generalize results about binary sequences of length 2p and evaluate the linear complexity and autocorrelation properties of generalized cyclotomic binary sequences of length 2p. We show that in most cases these sequences have high linear complexity and poor autocorrelation performance.
متن کامل