一类周期为pq阶为2的Whiteman广义分圆序列研究
doi: 10.3724/SP.J.1146.2008.01096
Study on a Class of Whiteman-Generalized Cyclotomic Sequence with Length pq and Order Two
-
摘要: 线性复杂度是度量序列随机性质最重要的指标之一。该文基于Whiteman-广义分圆，构造了一类周期为pq阶为2的广义分圆序列。证明了适当的选取参数p和q，该类序列的线性复杂度的下界为pq-p-q+1，且该类序列为平衡序列。最后指出了准确计算该序列的线性复杂度所必须解决的问题。Abstract: Linear complexity is one of the most important indexes for measuring the randomness properties of sequences. Based on Whiteman-generalized cyclotomy, a new class of generalized cyclotomic sequences with length qp and order 2 is constructed. It is proved that the lower bound of linear complexity of the sequence is pq-p-q+1 with the proper selection of parameters p and q, and the sequence has balance property. Finally, this paper points out the method for determine linear complexity.
-
Cusick T, Ding C, and Renvall A. Stream Ciphers andNumber Theory[M]. Elsevier/North-Holland. North-HollandMathematical Library 55, 1998: 195-226.[2]Ding C and Helleseth T. On cyclotomic generator of order r[J].Information Processing Letters.1998, 66(1):21-25[3]Whiteman A L. A family of difference sets [J]. Illinois Journalof Mathematics, 1962, 6(2): 107-121.[4]Ding C and Helleseth T. New generalized cyclotomy and itsapplications[J].Finite Fields and Their Applications.1998,4(2):140-166[5]Ding C. Linear complexity of generalized cyclotomic binarysequences of order 2[J].Finite Fields and Their Applications.1997, 3(2):159-174[6]Bai E J, Liu X J, and Xiao G Z. Linear complexity of newgeneralized cyclotomic sequences of order of length pq[J].IEEE Transactions on Information Theory.2005, 51(5):1849-1853[7]Ding C. Autocorrelation values of generalized cyclotomicsequences of order two[J].IEEE Transactions on InformationTheory.1998, 44(4):1699-1702[8]Li S Q, Chen Z X, and Sun R, et al.. On the randomness ofgeneralized cyclotomic sequences of order two and length pq[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences.2007, E90-A(9):2037-2041[9]Li S Q, Chen Z Q, and Fu X T, et al.. Autocorrelation valuesof new generalized cyclotomic sequences of order two andlength pq [J].Journal of Computer Science and Technology.2007, 22(6):830-834[10]Chen Z X and Li S Q. Some notes on generalized cyclotomicsequences of length pq[J].Journal of Computer Science andTechnolog.2008, 23(5):843-850[11]Yan T J, Li S Q, and Xiao G Z. On the linear complexity ofgeneralized cyclotomic sequences with the period m p [J].Applied Mathematics Letters.2008, 21(2):187-193 -
计量
- 文章访问数: 3512
- HTML全文浏览量: 124
- PDF下载量: 701
- 被引次数: 0
下载:
