| 环F4+uF4上线性码及其对偶码的Gray象 |
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| 引用本文： | 刘修生,刘花璐.环F4+uF4上线性码及其对偶码的Gray象[J].通信学报,2012(8):134-137. |
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| 作者姓名： | 刘修生 刘花璐 |
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| 作者单位： | 湖北理工学院数理学院 |
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| 基金项目： | 湖北省教育厅自然科学重点项目基金资助(B20114410)~~ |
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| 摘 要： | 研究了环F4+uF4与域F4上的线性码,利用环F4+uF4上码C的Gray重量wG,Gray距离d G和(F4+uF4)n到F4 2n的Gray映射φ,证明了环F4+uF4上线性码C及其对偶码的Gray像φ(C)为F4上的线性码和对偶且dH G(φ(C))dG(C)。同时,给出了F4+uF4上循环码C的Gray像φ(C)为F4上的2-拟循环码。
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| 关 键 词： | 线性码 对偶码 Gray重量 Gray映射 |
Gray images of the linear codes and their dual codes over F4+uF4 |
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| LIU Xiu-sheng,LIU Hua-lu.Gray images of the linear codes and their dual codes over F4+uF4[J].Journal on Communications,2012(8):134-137. |
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| Authors: | LIU Xiu-sheng LIU Hua-lu |
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| Affiliation: | (School of Math.and Physics,Hubei Polytechnic University,Huangshi 435003,China) |
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| Abstract: | The linear codes over ring F4+uF4 and field F4 were studied.By using the Gray weight wG,the Gray distance dG of codes C over F4+uF4,and the Gray map φ from (F4+uF4)n to F42n,the Gray image φ(C)of linear codes C over F4+uF4 were linear codes over F4 as well,dH(φ(C)) dG(C),and the proposition that linear codes φ(C) were the dual codes of φ(C) were showed.Furthermore,the Gray image φ(C) of cyclic codes C over F4+uF4 ere the 2-quasi cyclic codes over F4. |
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| Keywords: | linear code dual code Gray weight Gray map |
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