| 环F_2+uF_2+u~2F_2上的常循环码和循环码的Gray象 |
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| 引用本文： | 梁华.环F_2+uF_2+u~2F_2上的常循环码和循环码的Gray象[J].淮阴师范学院学报(自然科学版),2010,9(3):189-191. |
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| 作者姓名： | 梁华 |
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| 作者单位： | 淮阴师范学院,数学科学学院,江苏,淮安,223300 |
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| 基金项目： | 国家自然科学基金项目，教育部科学技术研究重点项目，江苏省自然科学基金项目 |
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| 摘 要： | 通过构造Gray映射Φ,研究了环R=F2+uF2+u2F2上的常循环码和循环码.给出了环R上码是常循环码的一个充分必要条件,证明了环R上长为n的码C是循环码当且仅当Φ(C)是域F2上指标为4长为4n的准循环码.特别的,环R上长为n的线性循环码的Gray像是F2上指标为4长为4n的线性准循环码.
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| 关 键 词： | 循环码 常循环码 准循环码 Gray映射 |
The Gray Images of Constacyclic and Cyclic Codes over F2+uF2+u2F2 |
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| LIANG Hua.The Gray Images of Constacyclic and Cyclic Codes over F2+uF2+u2F2[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2010,9(3):189-191. |
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| Authors: | LIANG Hua |
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| Institution: | LIANG Hua(School of Mathematical Science,Huaiyin Normal Univesity,Huaian Jiangsu 223300,China) |
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| Abstract: | By constructing the Gray map Φ,constacyclic and cyclic codes over the ring R=F2+uF2+u2F2 are studied.A necessary and sufficient condition for a code to be constacyclic over R is given.It is proved that a code C of length n over R is a cyclic code if and only if Φ(C) is a quasi-cyclic code over F2 of index 4 and length 4n. In particular,the Gray image of a linear cyclic code of length n over R is a linear quasi-cyclic code of index 4 and length 4n over F2. |
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| Keywords: | cyclic code constacyclic code quasi-cyclic code Gray map |
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