Hulls of constacyclic codes over finite non-chain rings and their applications in quantum codes construction

We study hulls of constacyclic codes of length n over a finite non-chain ring Fq+vFq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_q+v{\mathbb {F}}_q$$\end{document} with respect to the Euclidean and Hermitian inner products, where v2=v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v<^>2=v$$\end{document}. Under a special Gray map from Fq+vFq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_q+v{\mathbb {F}}_q$$\end{document} to Fq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}<^>2_q$$\end{document}, dimensions of hulls of Gary images of constacyclic codes are obtained. Some new quantum error-correcting codes (QECCs) with good parameters are constructed by the quantum construction X method under the Euclidean and Hermitian inner products, respectively. Some of these QECCs are MDS with the minimum distance greater than q2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{q}{2}$$\end{document}, and a few of these QECCs are MDS with the minimum distance equal to q.