2-Adic Complexity of Two Classes of Generalized Cyclotomic Binary Sequences with Order 4

Xiaoni DU  Liping ZHAO  Zhihua NIU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.11   pp.1566-1570
Publication Date: 2019/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1566
Type of Manuscript: LETTER
Category: Digital Signal Processing
finite field,  binary sequences,  cyclotomy sequences,  2-adic complexity,  

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Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and 2-adic complexity, have been widely applied to designing reliable stream ciphers. In this paper, we explicitly determine the 2-adic complexities of two classes of generalized cyclotomic binary sequences with order 4. Our results show that the 2-adic complexities of both of the sequences attain the maximum. Thus, they are large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers. We also present some examples to illustrate the validity of the results by Magma programs.