A note on self-dual negacyclic codes of length ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^s$$\end{document} over [inline-graphic not available: see fulltext]

Self-dual cyclic codes over rings and their generalizations have become of interest due to their rich algebraic structures and wide applications. Cyclic and self-dual cyclic codes over the ring [inline-graphic not available: see fulltext] have been quite well studied, where p is a prime, k is a positive integer, and u2=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^2=0$$\end{document}. We focus on negacyclic codes over [inline-graphic not available: see fulltext], where p is an odd prime and k is a positive integer. An alternative and explicit algebraic characterization of negacyclic codes of length ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^s$$\end{document} over [inline-graphic not available: see fulltext] is presented. Based on this result, representation and enumeration of self-dual negacyclic codes of length ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^s$$\end{document} over [inline-graphic not available: see fulltext] are given under both the Euclidean and Hermitian inner products.