| 环F_(p~k)+uF_(p~k)+u~2F_(p~k)上的常循环码和循环码 |
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| 引用本文： | 梁华,唐元生.环F_(p~k)+uF_(p~k)+u~2F_(p~k)上的常循环码和循环码[J].数学的实践与认识,2012,42(24). |
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| 作者姓名： | 梁华 唐元生 |
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| 作者单位： | 1. 淮阴师范学院数学科学学院,江苏淮安,223300
2. 扬州大学数学科学学院,江苏扬州,225002 |
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| 摘 要： | 记环R=F_(p~k)+uF_(p~k)+u~2F_(p~k),定义了一个从R~n到F_(p~k)~(2np~k)的Gray映射.利用Gray映射的性质,研究了环R上(1-u~2)-循环码和循环码.证明了环R上码是(1-u~2)-循环码当且仅当它的Gray象是F_(p~k)上的准循环码.当(n,p)=1时,证明了环R上的长为n的线性循环码的Gray象置换等价于域F_(p~k)上的线性准循环码.
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| 关 键 词： | 线性码 循环码 常循环码 准循环码 Gray映射 |
Constacyclic and Cyclic Codes over Fpk+uFpk+u2Fpk |
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| LIANG Hua
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TANG Yuan-sheng.Constacyclic and Cyclic Codes over Fpk+uFpk+u2Fpk[J].Mathematics in Practice and Theory,2012,42(24). |
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| Authors: | LIANG Hua TANG Yuan-sheng |
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| Abstract: | Let R=F_(p~k)+uF_(p~k) +u~2F_(p~k),a Gray map from R~n to F_(p~k)~(2np~k) is defined.Base on the property of Gray map,(1-u~2)-cychc and cyclic codes over R are studied.It is proved that a code over R is a(1-u~2)-cyclic code if and only if its Gray image is a quasi-cyclic code over F_(p~k).It is also proved that if(n,p) = 1,the Gray image of a linear cyclic code of length n over R is equivalent to a linear quasi-cyclic code over F_(p~k). |
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| Keywords: | linear code cyclic code constacyclic code quasi-cyclic code gray map |
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