One weight Z2Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_2\mathbb {Z}_4$$\end{document} additive codes

被引：0
作者：
Steven T. Dougherty
Hongwei Liu
Long Yu
机构：
[1] University of Scranton,Department of Mathematics
[2] Central China Normal University,School of Mathematics and Statistics
来源：
Applicable Algebra in Engineering, Communication and Computing | 2016年 / 27卷 / 2期
关键词：
One weight additive codes; Dual codes; Gray map; 94B60; 94B05;
D O I：
10.1007/s00200-015-0273-4
中图分类号：
学科分类号：
摘要：
We study one weight Z2Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_2\mathbb {Z}_4$$\end{document} additive codes. It is shown that the image of an equidistant Z2Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_2\mathbb {Z}_4$$\end{document} code is a binary equidistant code and that the image of a one weight Z2Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_2\mathbb {Z}_4$$\end{document} additive code, with nontrivial binary part, is a linear binary one weight code. The structure and possible weights for all one weight Z2Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_2\mathbb {Z}_4$$\end{document} additive codes are described. Additionally, a lower bound for the minimum distance of dual codes of one weight additive codes is obtained.
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页码：123 / 138
页数：15
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