New EAQEC codes from LCP of codes over finite non-chain rings

In this paper, we first study the linear complementary pair (abbreviated to LCP) of codes over finite non-chain rings Ru,v,q=Fq+uFq+vFq+uvFq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{u,v,q}={\mathbb {F}}_q+u{\mathbb {F}}_q+ v{\mathbb {F}}_q+uv{\mathbb {F}}_q$$\end{document} with u2=u,v2=v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u<^>2=u,v<^>2=v$$\end{document}. Then we provide a method of constructing entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes from an LCP of codes of length n over Ru,v,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{u,v,q}$$\end{document} using CSS. To enrich the variety of available EAQEC codes, some new EAQEC codes are given in the sense that their parameters are different from all the previous constructions.