| 环Z_p[u]/(u~(k+1))上循环码的Gray象 |
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| 引用本文： | 梁华,唐元生.环Z_p[u]/(u~(k+1))上循环码的Gray象[J].数学的实践与认识,2013,43(5). |
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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R=Z_pu]/(u~(k+1)),定义了从R~n到Z_p~(np~k)的Gray映射.利用Gray映射的性质,研究了环R上任意长循环码.证明了环R上任意长码是循环码当且仅当它的Gray象是域Z_p上的准循环码.特别的,环R上的线性循环码的Gray象是Z_p上的线性准循环码.
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| 关 键 词： | 线性码 循环码 准循环码 Gray映射 |
The Gray Images of Cyclic Codes over Zp[u]/(uk+1) |
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| LIANG Hua
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TANG Yuan-sheng.The Gray Images of Cyclic Codes over Zp[u]/(uk+1)[J].Mathematics in Practice and Theory,2013,43(5). |
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| Authors: | LIANG Hua TANG Yuan-sheng |
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| Abstract: | Let R = Z_pu]/(u~(k+1)).A Gray map from R~n to Z_p~(np~k) is defined.Base on the property of Gray map,cyclic codes of arbitrary length over.R are studied.It is proved that a code of arbitrary length over R is a cyclic code if and only if its Gray image is a quasi-cyclic code over Z_p.In particular,the Gray image of a linear cyclic code overR is a linear quasi-cyclic code over Z_p. |
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| Keywords: | linear code cyclic code quasi-cyclic code gray map |
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