吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (3): 521-530.

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基于经典线性码构造的纠缠辅助量子码

林晶晶, 唐西林   

  1. 华南理工大学 数学学院, 广州 510640
  • 收稿日期:2021-07-09 出版日期:2022-05-26 发布日期:2022-05-26
  • 通讯作者: 唐西林 E-mail: xltang@scut.edu.cn

Entanglement-Assisted Quantum Codes Constructed by Classical Linear Codes

LIN Jingjing, TANG Xilin   

  1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2021-07-09 Online:2022-05-26 Published:2022-05-26

摘要: 首先, 利用有限域Fq上参数为[n,k,d]经典线性码C的线性互补对偶(LCD)线性子码的一个正交基, 构造一类参数为[[n+l,k-h,d′;n-k
-h+l]]的纠缠辅助量子码, 其中h=dim(HullE(C)), 0≤l≤k-h, d≤d′≤d+l. 特别地, 当经典线性码C为Euclide对偶包含线性码时, 存在一个参数为[[n+l,2k-n,d′;l]]的纠缠辅助量子码, 其中0≤l≤2k-n, d≤d′≤d+l. 其次, 通过对有限域Fq上参数为[n,k,d]的Euclide对偶包含线性码C的校验矩阵H作一类变换, 构造另一类参数为[[n+l,2k-n+l,d′;2l]]的纠缠辅助量子码, 其中0≤l≤n-k, d≤d′≤d+l.

关键词: 纠缠辅助量子码, Euclide对偶, LCD码, 校验矩阵, 线性码

Abstract: Firstly, a class of entanglement-assisted quantum codes with parameters [[n+l,k-h,d′;n-k-h+l]] are constructed by using an orthogonal basis of the linear complementary dual (LCD) linear subcode of the classical linear code C with parameters [n,k,d]over a finite field Fq, where h=dim(HullE(C)), 0≤l≤k-h, d≤d′≤d+l. In particular, when the classical linear code C is Euclidean dual-containing linear code, there are entanglement-assisted quantum codes with parameters [[n+l,2k-n,d′;l]], where 0≤l≤2k-n, d≤d′≤d+l. Secondly, by making a kind of transformation on the parity check matrix H of Euclidean dual-containing linear code C with parameters [n,k,d], another kind of entanglement-assisted quantum codes with parameters [[n+l,2k-n+l,d′;2l]] are constructed, in which 0≤l≤n-k, d≤d′≤d+l.

Key words: entanglement-assisted quantum codes, Euclidean duality, LCD codes, parity-check matrix, linear codes

中图分类号: 

  • O236.2