Constructions of non-binary Golay complementary pairs of new lengths

A pair of sequences is called a Golay complementary pair (GCP), when it has zero aperiodic auto-correlation function (AACF) sum at every non-zero time shift. Due to its low peak-to-mean envelope power ratio (PMEPR), which is bounded by 2, it is used in many wireless communication applications. In this paper, we present direct constructions of 4h-ary (h >= 1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(h\ge 1)$$\end{document} GCPs of lengths of the forms 3x2m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 2<^>{m}$$\end{document} and 11x2m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$11\times 2<^>{m}$$\end{document}, (m >= 1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m\ge 1)$$\end{document} using multi-variable extended Boolean functions (EBFs). We have also provided the generating functions of the complementary mates for the proposed GCPs.