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Hamming distance of repeated-root constacyclic codes of length $$2p^s$$2ps over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$Fpm+uFpm
Applicable Algebra in Engineering, Communication and Computing ( IF 0.6 ) Pub Date : 2020-04-24 , DOI: 10.1007/s00200-020-00432-0
Hai Q. Dinh , A. Gaur , Indivar Gupta , Abhay K. Singh , Manoj Kumar Singh , Roengchai Tansuchat

Let p be an odd prime, and δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document} be an arbitrary unit of the finite chain ring Fpm+uFpm(u2=0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)$$\end{document}. The Hamming distances of all δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}-constacyclic codes of length 2ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2p^s$$\end{document} over Fpm+uFpm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$\end{document} are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS repeated-root δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}-constacyclic codes of length 2ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2p^s$$\end{document} over Fpm+uFpm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}$$\end{document}.

中文翻译:

长度为 $$2p^s$$2ps 的重复根恒循环码在 $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$ 上的汉明距离$Fpm+uFpm

{F}}_{p^m}$$\end{document} 完全确定。我们提供了一些示例,其中一些代码具有比现有代码更好的参数。作为应用程序,
更新日期:2020-04-24
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