| 环GR(4,2)上一类负循环码的Gray象 |
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| 引用本文： | 开晓山,朱士信.环GR(4,2)上一类负循环码的Gray象[J].系统科学与数学,2010,30(3):334-340. |
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| 作者姓名： | 开晓山 朱士信 |
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| 作者单位： | 合肥工业大学数学学院,合肥,230009 |
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| 基金项目： | 国家自然科学基金，工科数学基础课应用型学习研究项目，安徽高校省级自然科学研究重点项目，合肥工业大学科学研究发展基金 |
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| 摘 要： | 研究了GR(4,2)上长为2~s的负循环码的Gray象,证明了GR(4,2)上长为2~s的负循环码的Gray象是F_4上长为2~(s+2)指数为2的准循环码.通过计算GR(2~a,m)上长为2~s的负循环码的齐次距离,确定了GR(4,2)上长为2~s的负循环码的Gray象的汉明距离.
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| 关 键 词： | Gray象 汉明距离 齐次距离 负循环码 准循环码. |
| 收稿时间： | 2008-11-6 |
GRAY IMAGES OF A CLASS OF NEGACYCLIC CODES OVER GR(4,2) |
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| KAI Xiaoshan ZHU Shixin.GRAY IMAGES OF A CLASS OF NEGACYCLIC CODES OVER GR(4,2)[J].Journal of Systems Science and Mathematical Sciences,2010,30(3):334-340. |
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| Authors: | KAI Xiaoshan ZHU Shixin |
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| Institution: | School of Mathematics, Hefei University of Technology, Hefei 230009 |
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| Abstract: | This paper investigates the Gray images of negacyclic codes of length $2^{s}$ over $GR(4,2)$. It is proved that the Gray image of a negacyclic code of length $2^{s}$ over $GR(4,2)$ is a distance-invariant linear quasicyclic code of index 2 and length $2^{s+2}$ over $F_{4}$. The homogeneous distances of negacyclic codes of length $2^{s}$ over $GR(2^{a},m)$ in general are calculated. The homogeneous distances are used to determine the Hamming distances of the Gray images of negacyclic codes of length $2^{s}$ over $GR(4,2)$. |
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| Keywords: | Gray map Hamming distance homogeneous distance negacyclic codes quasicyclic codes |
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