Some new classes of quaternary sequences with low autocorrelation property via two binary cyclotomic sequences

A quaternary sequence is said to be good if its maximum nontrivial autocorrelation is very low relative to its period. In this paper, we present some new classes of quaternary sequences with low autocorrelation of period N via two binary cyclotomic sequences, where N≡1(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\equiv 1~(\text {mod}~4)$$\end{document} is an odd prime. Furthermore, we determine the linear complexity and minimal polynomials of these quaternary sequences over F22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{2^{2}}$$\end{document} as well.