MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

Luo Gaojun; Cao Xiwang; Chen Xiaojing

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MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

机译：具有任意尺寸的船体的MDS代码及其量子误差校正

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摘要

The hull of linear codes has promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect to the Euclidean inner product. Several infinite families of MDS codes with hulls of arbitrary dimensions are presented. As an application, using these MDS codes with hulls of arbitrary dimensions, we construct several new infinite families of entanglement-assisted quantum error-correcting codes with flexible parameters.

机译：线性编码的外壳在编码理论和量子编码理论中具有广阔的应用前景。在本文中，我们针对欧几里德内积，研究了有限域上的广义Reed-Solomon码和扩展的广义Reed-Solomon码的外壳。提出了具有无限尺寸的船体的MDS代码的几个无限族。作为应用程序，将这些MDS代码与任意尺寸的船体一起使用，我们可以构建具有可变参数的纠缠辅助量子纠错代码的几个新的无限系列。

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来源
《IEEE Transactions on Information Theory》 |2019年第5期|2944-2952|共9页
作者
Luo Gaojun; Cao Xiwang; Chen Xiaojing;
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作者单位

Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China;

Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China|Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China;

Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China;

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正文语种 eng
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关键词
Hull; generalized Reed-Solomon code; MDS code; entanglement-assisted quantum error-correcting code (EAQECC);

机译：船体;广义芦苇所罗门代码;MDS代码;纠缠辅助量子纠错码（eaqecc）;

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专利

1. MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction [J] . Luo Gaojun, Cao Xiwang, Chen Xiaojing IEEE Transactions on Information Theory . 2019,第5期

机译：具有任意尺寸的船体及其量子误差校正的MDS代码
2. Encoding an arbitrary state in a [7,1,3] quantum error correction code [J] . Sidney D. Buchbinder, Channing L. Huang, Yaakov S. Weinstein Quantum information processing . 2013,第2期

机译：用[7,1,3]量子纠错码编码任意状态
3. Some new entanglement-assisted quantum error-correcting MDS codes from generalized Reed-Solomon codes [J] . Quantum information processing . 2020,第7期

机译：来自广义芦苇型码代码的一些新的纠缠辅助量子纠错MDS代码
4. Three and four-dimensional parity-check codes for correction and detection of multiple errors [C] . Anne N.B., Utthaman Thirunavukkarasu, Latifi S. Information Technology: Coding and Computing, 2004. Proceedings. ITCC 2004. International Conference on . 2004

机译：用于纠正和检测多个错误的三维奇偶校验码
5. Codeword stabilized quantum codes and their error correction. [D] . Li, Yunfan. 2010

机译：码字稳定的量子码及其纠错。
6. Erratum: CORRIGENDUM: Fault-tolerant quantum computation with a soft-decision decoder for error correction and detection by teleportation [O] . Hayato Goto, Hironori Uchikawa -1

机译：勘误：勘误：具有软判决解码器的容错量子计算用于纠错和通过隐形传送进行检测
7. Encoding an Arbitrary State in a [7,1,3] Quantum Error Correction Code [O] . Buchbinder, Sidney D., Huang, Channing L., Weinstein, Yaakov S. 2011

机译：在[7,1,3]量子纠错码中编码任意状态

MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

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