Linear Complexity of New Generalized Cyclotomic Sequences of Order Two with Odd Length

Yu-qian ZHOU  Fei GAO  Jie ZHANG  Qian-yan WEN  Zu-ling CHANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.8   pp.1639-1644
Publication Date: 2016/08/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.1639
Type of Manuscript: LETTER
Category: Spread Spectrum Technologies and Applications
Keyword: 
new generalized cyclotomic sequences,  minimal polynomial,  linear complexity,  

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Summary: 
Based on the generalized cyclotomy of order two with respect to n=p1e1+1p2e2+1ptet+1, where p1, p2, …,pt are pairwise distinct odd primes and e1, e2,…, et are non-negative integers satisfying gcd (piei (pi-1), pjej (pj-1)) = 2 for all ij, this paper constructs a new family of generalized cyclotomic sequences of order two with length n and investigates their linear complexity. In the view of cascade theory, this paper obtains the linear complexity of a representative sequence.