The cross-correlation spectrum of ternary perfect sequences and their decimations

In this paper, we consider the cross-correlation spectrum between a ternary perfect sequence having terms in {-1,0,1}\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\{-1,0,1\}$$\end{document} and its d-decimation, where d=3k+12\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d={3<^>k+1\over 2}$$\end{document}. We prove that the cross-correlation function between this pair of ternary sequences has three different values. In addition, we propose a new class of ternary perfect sequences, based on the derived cross-correlation.