EAQECCs derived from constacyclic codes over finite non-chain rings

Entanglement-assisted quantum error-correcting codes (EAQECCs) not only can boost the performance of stabilizer quantum error-correcting codes but also can be derived from arbitrary classical linear codes by loosing the self-orthogonal condition and using pre-shared entangled states between the sender and the receiver. It is a challenging work to construct optimal EAQECCs and determine the required number of pre-shared entangled states. Let Rt=Fq2+vFq2+v2Fq2+& ctdot;+vtFq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{t}=\mathbb {F}_{q<^>{2}}+v\mathbb {F}_{q<^>{2}}+v<^>{2}\mathbb {F}_{q<^>{2}}+\cdots +v<^>{t}\mathbb {F}_{q<^>{2}}$$\end{document}, where q is an odd prime power and vt+1=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v<^>{t+1}=1$$\end{document}. Based on the generalized Gray map that is provided from Rt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{t}$$\end{document} to Fq2t+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q<^>{2}}<^>{t+1}$$\end{document}, some new optimal EAQECCs are constructed from the Gray images of v-constacyclic codes over Rt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{t}$$\end{document}. Compared with the known ones, our codes have better parameters.