Hamming distance of repeated-root 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}

被引:0
作者
Hai Q. Dinh
A. Gaur
Indivar Gupta
Abhay K. Singh
Manoj Kumar Singh
Roengchai Tansuchat
机构
[1] Ton Duc Thang University,Faculty of Mathematics and Statistics
[2] Ton Duc Thang University,Division of Computational Mathematics and Engineering, Institute for Computational Science
[3] University of Delhi (DU),Department of Mathematics
[4] SAG,Department of Applied Mathematics
[5] DRDO,Centre of Excellence in Econometrics, Faculty of Economics
[6] Indian Institute of Technology (ISM),undefined
[7] Chiang Mai University,undefined
关键词
Repeated-root codes; Constacyclic codes; Hamming distance; Finite chain rings;
D O I
10.1007/s00200-020-00432-0
中图分类号
学科分类号
摘要
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}.
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收藏
页码:291 / 305
页数:14
相关论文
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