| 环F2+uF2+vF2上线性码广义Gray像 |
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| 引用本文： | 唐刚.环F2+uF2+vF2上线性码广义Gray像[J].数学杂志,2012,32(3):567-570. |
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| 作者姓名： | 唐刚 |
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| 作者单位： | 湖北理工学院数理学院,湖北黄石,435002 |
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| 摘 要： | 本文定义了环F2+uF2+vF2到域F2的广义Gray映射φ像,研究了环F2+uF2+vF2上线性码的广义Gray像.利用广义Gray映射φ的线性性,证明了环F2+uF2+vF2上线性码C的广义Gray像φ(C)满足dH(C)=dH(φ(C))且φ(C⊥)φ(C)⊥.同时,给出了F2+uF2+vF2上循环码C的广义Gray像φ(C)为F2上的4-拟循环码.
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| 关 键 词： | 线性码 广义Gray映射 拟循环码 |
THE GENERALIZED GRAY IMAGES OF LINEAR CODES OVER F2 + uF2 + vF2 |
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| TANG Gang.THE GENERALIZED GRAY IMAGES OF LINEAR CODES OVER F2 + uF2 + vF2[J].Journal of Mathematics,2012,32(3):567-570. |
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| Authors: | TANG Gang |
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| Institution: | TANG Gang(School of Math.and Physics,Hubei Polytechnic University,Huangshi 435003,China) |
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| Abstract: | The generalized Grayφis defined from F2+uF2+vF2 to F4 n 2.The generalized Gray images of linear codes over F2+uF2+vF2 are studied.By using the linearlity of the generality Grayφ,it is proved that the generalized Gray imagesφ(C)of linear codes C over F2+uF2+vF2 are linear codes over F2 and dH(C)=dH(φ(C)).Furthermore,we obtain that φ(C⊥)φ(C)⊥and the generalized Gray imagesφ(C)of cyclic codes C over F2+uF2+vF2 are the 4-quasi-cyclic codes over F2. |
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| Keywords: | linear code generalized Gray map quasi cyclic code |
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