| 环Z2+uZ2+u2Z2上的斜循环码 |
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| 引用本文： | 李锦,朱士信.环Z2+uZ2+u2Z2上的斜循环码[J].合肥工业大学学报(自然科学版),2011(11):1745-1748. |
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| 作者姓名： | 李锦 朱士信 |
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| 作者单位： | 合肥工业大学数学学院; |
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| 基金项目： | 国家自然科学基金资助项目(60973125); 高等学校博士学科点专项科研基金资助项目(200080359003) |
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| 摘 要： | 文章研究的是环R=Z2 +uZ2 +u2Z2上一类广义的循环码——斜循环码；首先利用环R构造了一个非交换的多项式环Rx,θ],然后讨论了R上斜循环码与Rn=RX,θ]/(Xn-1)左理想的关系,给出了斜循环码的生成多项式,以及环R上斜循环码是可逆码的充要条件,并考虑了斜循环码的对偶码.
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| 关 键 词： | 斜循环码 可逆码 斜多项式环 对偶码 |
Skew cyclic codes over the ring Z_2+uZ_2+u~2Z_2 |
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| LI Jin,ZHU Shi-xin.Skew cyclic codes over the ring Z_2+uZ_2+u~2Z_2[J].Journal of Hefei University of Technology(Natural Science),2011(11):1745-1748. |
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| Authors: | LI Jin ZHU Shi-xin |
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| Institution: | LI Jin,ZHU Shi-xin(School of Mathematics,Hefei University of Technology,Hefei 230009,China) |
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| Abstract: | This paper studies a class of generalized cyclic codes over the ring R=Z2+uZ2+u2Z2,which are called skew cyclic codes.The ring R is used to construct a noncommutative skew polynomial ring R.Then the relation between the skew cyclic codes over the ring R and the left ideal as Rn=R/(Xn-1) is studied,and the generator polynomial of the skew cyclic codes is given.The necessary and sufficient condition for a skew cyclic code to be a reversible code is introduced,and the dual codes of the skew cyclic codes are di... |
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| Keywords: | skew cyclic code reversible code skew polynomial ring dual code |
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