| 环F_2+uF_2+u~2F_2上线性码的广义Gray像 |
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| 引用本文： | 张晓燕.环F_2+uF_2+u~2F_2上线性码的广义Gray像[J].数学的实践与认识,2011,41(9). |
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| 作者姓名： | 张晓燕 |
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| 作者单位： | 黄石理工学院数理学院,湖北黄石,435002 |
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| 摘 要： | 摘要:引入了环F_2+uF_2+u~2F_2与F_2之间的广义Gray映射,利用环F_2+uF_2+u~2F_2上线性码的生成矩阵得出了广义Gray像φ(C)的生成矩阵,证明了F_2+uF2+u2F2上线性码自正交码的广义Gray像仍为自正交码和F_2+uF_2+u~2F_2上循环码的广义Gray像是F_2上的准循环码.
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| 关 键 词： | 线性码 生成矩阵 广义Gray映射 循环码 |
Generalized Gray Images of the Linear Codes Over the Ring F2 + uF2 + u2F2 |
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| ZHANG Xiao-yan.Generalized Gray Images of the Linear Codes Over the Ring F2 + uF2 + u2F2[J].Mathematics in Practice and Theory,2011,41(9). |
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| Authors: | ZHANG Xiao-yan |
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| Abstract: | In this paper,we introduce the generalized Gray map from F_2+uF_2+u~2F_2 to F_2,then gets the generator matrix of the generalized Gray imageφ(C)from the generator matrix of the linear code C over F_2+uF_2+u~2F_2,and proves that the generalized Gray imagesφ(C)of self-orthogonal C over F_2+uF_2+u~2F_2 are self-orthogonal too.Moreover, the generalized Gray imagesφ(C)of cyclic codes C are quasi-cyclic codes over F_2. |
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| Keywords: | linear code generator matrix the generalized Gray map cyclic code |
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