A Construction of Binary Cyclotomic Sequences Using Extension Fields

Zhixiong CHEN  Xiaoni DU  Rong SUN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.2   pp.663-667
Publication Date: 2009/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.663
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
stream ciphers,  cyclotomic sequences,  pseudorandom binary sequences,  character sums,  correlation,  

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Based on the cyclotomy classes of extension fields, a family of binary cyclotomic sequences are constructed and their pseudorandom measures (i.e., the well-distribution measure and the correlation measure of order k) are estimated using certain exponential sums. A lower bound on the linear complexity profile is also presented in terms of the correlation measure.