| 量子纠错码的等价和保距同构 |
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| 引用本文： | 刘太琳,温巧燕.量子纠错码的等价和保距同构[J].数学学报,2008,51(1):1-10. |
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| 作者姓名： | 刘太琳 温巧燕 |
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| 作者单位： | [1]山东财政学院统计与数理系,济南250014 [2]北京邮电大学理学院,北京100876 |
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| 基金项目： | 国家高技术研究发展863计划（2006AA012419）;国家自然科学基金重大研究计划（90604023）;教育部高校博士点基金（20040013007）;现代通信国家重点实验室基金（9140C1101010601）;ISN开放基金 |
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| 摘 要： | 研究了量子纠错码的等价性和保距同构,推广了Bogart等人的一些概念,并给出若干基本定理,这些定理对进一步研究量子码的等价性和保距同构是非常有用的.在此基础上构造出一个反例,证明了在量子情形下,MacWmiams的一个重要定理不成立.
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| 关 键 词： | 辛码 量子(稳定子)码 等价 保距同构 |
| 文章编号： | 0583-1431（2008）01-0001-10 |
| 收稿时间： | 2006-11-10 |
| 修稿时间： | 2007-07-25 |
Isometries and Equivalences of Quantum Codes |
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| Tai Lin LIU,Qiao Yah WEN.Isometries and Equivalences of Quantum Codes[J].Acta Mathematica Sinica,2008,51(1):1-10. |
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| Authors: | Tai Lin LIU Qiao Yah WEN |
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| Institution: | Tai Lin LIU Department of Statistics and Mathematics,Shandong Finance Institute,Ji'nan 250014,P.R.China School of Science,Beijing University of Post and Telecommunications,Beijing 100876,P.R.China Qiao Yan WEN School of Science,Beijing University of Post and Telecommunications,Beijing 100876,P.R.China |
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| Abstract: | Some results on the isometries and equivalences of quantum codes are presented, one of which generalizes one of the results of Bogart et al., by these results, we construct an isometry of quantum codes which is not an equivalent mapping but preserves the symplectic inner product, i.e., a theorem of MacWilliams cannot be generalized to the quantum codes. |
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| Keywords: | symplectic codes quantum(stabilizer)codes isometries equivalences |
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