| 环Z4上自对偶码的构造 |
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| 引用本文： | 袁健,朱士信,开晓山.环Z4上自对偶码的构造[J].电子学报,2016,44(11):2807-2811. |
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| 作者姓名： | 袁健 朱士信 开晓山 |
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| 作者单位： | 1. 合肥工业大学数学学院, 安徽合肥 230009;
2. 东南大学移动通信国家重点实验室, 江苏南京 210096 |
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| 基金项目： | 国家自然科学基金(No．61370089)；东南大学移动通信国家重点实验室开放研究基金(No．2014D04)；安徽省自然科学基金(JZ2015AKZR0021，1508085SQA198) |
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| 摘 要： | 利用有限环Z4+vZ4（其中v2=1）上自对偶码，给出了一种构造Z4上自对偶码的方法.引入了（Z4+vZ4）n到Z42n的保距Gray映射，给出了Z4+vZ4上自对偶码的性质，证明了Z4+vZ4上长为n的自对偶码的Gray像是Z4上长为2n的自对偶码，由此构造了Z4上一些极优的类型I与类型Ⅱ自对偶码.
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| 关 键 词： | Gray映射 线性码 自对偶码 |
| 收稿时间： | 2015-07-08 |
A Method for Construction Self-dual Codes over Z4 |
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| YUAN Jian,ZHU Shi-xin,KAI Xiao-shan.A Method for Construction Self-dual Codes over Z4[J].Acta Electronica Sinica,2016,44(11):2807-2811. |
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| Authors: | YUAN Jian ZHU Shi-xin KAI Xiao-shan |
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| Affiliation: | 1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, Jiangsu 210096, China |
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| Abstract: | A Method for Construction self-dual codes over Z4 is proposed by using self-dual codes over the ring Z4 +vZ4 ,where v2 =1 .A Gray map from (Z4 +vZ4 )n to Z2n4 is introduced,and some properties about self-dual codes over Z4 +vZ4 are given.It showns that the Gray image of a self-dual code over Z4 +vZ4 of length n is a self-dual code over Z4 of length 2n.Further,some extremal Type I and Type Ⅱ codes over Z4 are constructed. |
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| Keywords: | Gray map linear codes self-dual codes |
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