一类特殊码长的非对称量子BCH码

doi:10.3969/j.issn.0372-2112.2019.11.011

电子学报 ›› 2019, Vol. 47 ›› Issue (11): 2311-2316.DOI: 10.3969/j.issn.0372-2112.2019.11.011

一类特殊码长的非对称量子BCH码

马月娜¹, 冯晓毅², 刘杨¹, 郭冠敏¹

1. 空军工程大学基础部, 陕西西安, 710051;
2. 西北工业大学电子信息学院, 陕西西安, 710072

收稿日期:2019-04-15 出版日期:2019-11-25
- 作者简介:
- 马月娜 女,1977年生于陕西西安,空军工程大学副教授,硕士生导师.主要研究方向为纠错码的性能与构造,纠错码在图像与视频处理中的应用.E-mail:mayuena2013@163.com;冯晓毅 女,1969年生于陕西蓝田,西北工业大学教授,博士生导师,电子信息学院副院长.主要研究方向为图像处理,计算机视觉,情感识别,雷达成像,嵌入式系统设计与应用.E-mail:fengxiao@nwpu.edu.cn
- 基金资助:
- 国家自然科学基金面上项目 (No.11471011); 国家自然科学基金青年项目 (No.11801564)

A Class of Special Code Length Asymmetric Quantum BCH Codes

MA Yue-na¹, FENG Xiao-yi², LIU Yang¹, GUO Guan-min¹

1. Department of Basic Sciences, Air Force Engineering University, Xi'an, Shaanxi 710051, China;
2. School of Electronics and Information, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China

Received:2019-04-15 Online:2019-11-25 Published:2019-11-25
- Supported by:
- National Natural Science Foundation of China (No.11471011); Youth Fund of National Natural Science Foundation of China (No.11801564)

摘要/Abstract

摘要： 非对称量子纠错码是针对量子通信中不同类型量子错误发生的概率而设计的有效编码方案.纠错性能良好的量子码在量子通信的真实性和可靠性方面起着决定性的作用.本文首先通过研究分圆陪集的性质确定出非本原狭义BCH码满足Hermitian对偶包含的条件；其次，利用推广的CSS构造法构造出一系列特殊码长的非对称量子BCH码；最后，给出了m分别为3和5的两类非对称量子BCH码维数，它们的z-距离远大于已有文献中的结论，因而提高了非对称量子信道中对相位错误的纠错能力.

关键词: 非对称量子BCH码, 非本原BCH码, Hermitian 对偶包含条件, CSS构造法

Abstract: Asymmetric quantum codes are an efficient coding scheme against different kinds of quantum errors in quantum communication, which occurs with different probability. The good quantum codes play a decisive role in ensuring the authenticity and reliability of quantum communication.In this paper, we first present Hermitian dual-containing conditions of the imprimitive narrow-sense BCH codes by a detailed analysis of cyclotomic cosets. Secondly, a series of asymmetric quantum BCH codes with special code length are constructed via the generalized CSS construction. Finally, dimensions of two types of asymmetric quantum BCH codes are determined for m as 3 and 5 respectively, whose z distances are much greater than the results in the literature. Hence, the error-correcting ability to the phase errors can be further improved.

Key words: asymmetric quantum code, imprimitive BCH code, Hermitian dual containing condition, CSS construction

中图分类号:

TN914.4

马月娜, 冯晓毅, 刘杨, 等. 一类特殊码长的非对称量子BCH码[J]. 电子学报, 2019, 47(11): 2311-2316.

MA Yue-na, FENG Xiao-yi, LIU Yang, et al. A Class of Special Code Length Asymmetric Quantum BCH Codes[J]. Acta Electronica Sinica, 2019, 47(11): 2311-2316.

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一类特殊码长的非对称量子BCH码

A Class of Special Code Length Asymmetric Quantum BCH Codes

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