A Class of Special Code Length Asymmetric Quantum BCH Codes

MA Yue-na; FENG Xiao-yi; LIU Yang; GUO Guan-min

doi:10.3969/j.issn.0372-2112.2019.11.011

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A Class of Special Code Length Asymmetric Quantum BCH Codes

更新时间：2025-07-16

- A Class of Special Code Length Asymmetric Quantum BCH Codes
- Acta Electronica Sinica Vol. 47, Issue 11, Pages: 2311-2316(2019)
- 作者机构：
  
  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
  3. 空军工程大学基础部,陕西,西安,710051
  4. 西北工业大学电子信息学院,陕西,西安,710072
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11471011);Youth Fund of National Natural Science Foundation of China (No.11801564)
- DOI：10.3969/j.issn.0372-2112.2019.11.011
  CLC： TN914.4
- Published Online：25 November 2019，
  
  Published：2019
- 稿件说明：
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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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2019.11.011.

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

分别为3和5的两类非对称量子BCH码维数，它们的

-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.

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

as 3 and 5 respectively

whose

distances are much greater than the results in the literature. Hence

the error-correctin

g ability to the phase errors can be further improved.

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