| 环F2+uF2上线性码及其对偶码的二元象 |
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| 引用本文： | 余海峰,朱士信. 环F2+uF2上线性码及其对偶码的二元象[J]. 电子与信息学报, 2006, 28(11): 2121-2123 |
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| 作者姓名： | 余海峰 朱士信 |
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| 作者单位： | 1. 合肥学院数理系,合肥,230022;合肥工业大学应用数学系,合肥,230009
2. 合肥工业大学应用数学系,合肥,230009 |
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| 基金项目： | 安徽省自然科学基金;安徽省教育厅自然科学基金 |
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| 摘 要： | 利用环F2＋uF2上线性码C的生成矩阵给出了码C的对偶码C^┴及其Gray象Ф（C）的生成矩阵，证明了环F2＋uF2上线性码及其对偶码的Gray象仍是对偶码。并由此给出了一个环F2＋uF2如上线性码为自对偶码的充要条件。
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| 关 键 词： | 线性码 对偶码 生成矩阵 Gray映射 |
| 文章编号： | 1009-5896(2006)11-2121-03 |
| 收稿时间： | 2005-03-08 |
| 修稿时间： | 2005-08-30 |
The Binary Images of the Linear Codes and Their Dual Codes Over F2+uF2 |
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| Yu Hai-feng,Zhu Shi-xin. The Binary Images of the Linear Codes and Their Dual Codes Over F2+uF2[J]. Journal of Electronics & Information Technology, 2006, 28(11): 2121-2123 |
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| Authors: | Yu Hai-feng Zhu Shi-xin |
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| Affiliation: | 1Dept.of Mathematics, Hefei University, Hefei 230022, China;2Dept.of Applied Mathematics, Hefei University of Technology, Hefei 230009, China |
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| Abstract: | Based on the generator matrix of linear codes C over , F2+uF2 the generator matrixes of the dual codes C and the Gray images (C) of the linear codes C are given, and the proposition that linear codes (C) are the dual codes of (C) are showed. By using this proposition, the necessary and sufficient condition of a linear code over F2+uF2 which is self-dual is obtained. |
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| Keywords: | Linear code Dual code Generator matrix Gray map |
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