Application of Constacyclic Codes Over the Semi Local Ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_{{p^m}}} + v{F_{{p^m}}}$$\end{document}

In this paper, we study the quantum codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_{{p^m}}}$$\end{document}, which are obtained from (λ1 + λ2)-constacyclic codes over the semi local ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_{{p^m}}} + v{F_{{p^m}}}$$\end{document}, where v2 = 1, p is odd prime. We decompose a (λ1 + λ2)-constacyclic code over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_{{p^m}}} + v{F_{{p^m}}}$$\end{document} into two constacyclic codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_{{p^m}}}$$\end{document} such as (λ1 + λ2)-constacyclic and (λ1–λ2)-constacyclic. We give the necessary and sufficient condition that the (λ1 + vλ2)-constacyclic codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_{{p^m}}} + v{F_{{p^m}}}$$\end{document} contain their duals. We give some examples of non binary quantum codes.