通信学报 ›› 2021, Vol. 42 ›› Issue (10): 182-188.doi: 10.11959/j.issn.1000-436x.2021194

• 学术论文 • 上一篇    下一篇

基于分圆陪集的量子BCH码的构造

邢莉娟, 李卓   

  1. 西安电子科技大学综合业务网国家重点实验室,陕西 西安 710071
  • 修回日期:2021-09-23 出版日期:2021-10-25 发布日期:2021-10-01
  • 作者简介:邢莉娟(1982- ),女,陕西西安人,博士,西安电子科技大学副教授,主要研究方向为量子信息论、量子通信、量子纠错码理论
    李卓(1980- ),男,陕西西安人,博士,西安电子科技大学教授,主要研究方向为量子计算、量子信息论、5G 中的编码调制技术
  • 基金资助:
    国家自然科学基金资助项目(61372072);111工程基金资助项目(B08038)

Construction of quantum BCH code based on cyclotomic coset

Lijuan XING, Zhuo LI   

  1. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China
  • Revised:2021-09-23 Online:2021-10-25 Published:2021-10-01
  • Supported by:
    The National Natural Science Foundation of China(61372072);The 111 Project(B08038)

摘要:

量子纠错码是克服量子消相干的主要手段,是实现量子计算机的关键技术。量子 BCH 码可以利用满足特定关系的经典码构造。首先推导了选择分圆陪集的一般性方法,给出了计算每一个分圆陪集包含元素个数的充要条件。然后给出了有限域Fq上利用CSS构造和Steane构造来构造量子BCH码的方法。最后将该方法扩展到有限域Fq2上,给出了利用Hermitian构造来构造量子BCH码的方法。与已有的结果相比,所提方法具有更好的码参数和更高的最小距离下界,可以得到大量新的量子 BCH 码。此外,所提方法还可以得到一类任意域上的量子最大距离可分码。

关键词: 量子BCH码, 分圆陪集, Steane构造, Hermitian构造

Abstract:

Quantum-error-correcting code can overcome quantum decoherence efficiently, which is the key technology to realize quantum computers.A series of quantum BCH code was proposed based on classical codes.First, a general way of well-chosen cyclotomic coset was introduced.A sufficient condition was given to calculate the number of elements in cyclotomic coset.Then, a series of quantum BCH (Bose-Chaudhuri-Hocquenghem) code over finite field Fq was constructed by CSS (Calderbank-Shor-Steane) construction and Steane construction.The results were extended to finite field Fq2 with Hermitian construction.Compared with the results in literature,the range of introduced cyclotomic coset is more wide, and the new quantum BCH code has higher dimensions and better lower bounds on minimum distances.Furthermore, a family of quantum maximum distance separable (quantum MDS) code over any finite fields is constructed.

Key words: quantum BCH code, cyclotomic coset, Steane construction, Hermitian construction

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