1. On the 2-adic complexity of cyclotomic binary sequences of order four.
- Author
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Sun, Fuqing, Yue, Qin, and Li, Xia
- Abstract
Let p≡1(mod4)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$p\equiv 1\pmod 4$$\end{document} be a prime. In this paper, we support a new method, i.e., a product of 2-adic values for four binary sequences, to determine the maximum evaluations of the 2-adic complexity in all almost balanced cyclotomic binary sequences of order four with period N=p\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N=p$$\end{document}, which are viewed as generalizing the results in Hu (IEEE Trans. Inf. Theory 60:5803–5804, 2014) and Xiong et al. (IEEE Trans. Inf. Theory 60:2399–2406, 2014) without the autocorrelation values of cyclotomic binary sequences of order four with period
p . By number theory we obtain two necessary and sufficient conditions about the 2-adic complexity of all balanced cyclotomic binary sequences of order four with period N=2p\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N=2p$$\end{document} and show the 2-adic complexity of several non-balanced cyclotomic binary sequences of order four with period 2p , which are viewed as generalizing the results in Zhang et al. (IEEE Trans. Inf. Theory 66:4613–4620, 2020). [ABSTRACT FROM AUTHOR]- Published
- 2023
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