Constacyclic codes over the ring Fq+vFq+v2Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$\end{document} and their applications of constructing new non-binary quantum codes

Let R=Fq+vFq+v2Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R={\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$\end{document} be a finite non-chain ring, where q is an odd prime power and v3=v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v^3=v$$\end{document}. In this paper, we propose two methods of constructing quantum codes from (α+βv+γv2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha +\beta v+\gamma v^{2})$$\end{document}-constacyclic codes over R. The first one is obtained via the Gray map and the Calderbank–Shor–Steane construction from Euclidean dual-containing (α+βv+γv2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha +\beta v+\gamma v^{2})$$\end{document}-constacyclic codes over R. The second one is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing (α+βv+γv2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha +\beta v+\gamma v^{2})$$\end{document}-constacyclic codes over R. As an application, some new non-binary quantum codes are obtained.