The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude

In 2008, a class of binary sequences of period N=4(2k-1)(2k+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=4(2^k-1)(2^k+1)$$\end{document} with optimal autocorrelation magnitude has been presented by Yu and Gong based on an m-sequence, the perfect sequence (0, 1, 1, 1) of period 4 and interleaving technique. In this paper, we study the 2-adic complexity of these sequences. Our result shows that it is larger than N-2⌈log2N⌉+4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N-2\lceil \mathrm {log}_2N\rceil +4$$\end{document} (which is far larger than N/2) and could attain the maximum value N if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.