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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 161-166.doi: 10.6040/j.issn.1671-9352.0.2022.351

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基于Z2pm上二阶广义割圆的量子可同步码

孙诗文1(),牟丹阳2   

  1. 1. 中国石油大学(华东)理学院，山东 青岛 266580
    2. 中国石油大学(华东)经济管理学院，山东 青岛 266580
  • 收稿日期:2022-06-23 出版日期:2023-12-20 发布日期:2023-12-19
  • 作者简介:孙诗文(1998—)，女，硕士研究生，研究方向为代数编码学. E-mail：winner_ssw@163.com
  • 基金资助:
    中国石油大学(华东)研究生创新工程项目(YCX2021137)

Quantum synchronizable codes from generalized cyclotomy of order two over Z2pm

Shiwen SUN1(),Danyang MOU2   

  1. 1. College of Science, China University of Petroleum (East China), Qingdao 266580, Shandong, China
    2. School of Economics and Management, China University of Petroleum (East China), Qingdao 266580, Shandong, China
  • Received:2022-06-23 Online:2023-12-20 Published:2023-12-19

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摘要：

基于Z2pm上的二阶广义割圆构造一类新型的量子可同步码，此类纠错码具有最优的纠正信息块同步错误的能力，其可同步能力总是其上界2pm。此外，这类码字对由量子噪声引起的比特错误和相位错误也具有一定的纠错能力。最后，给出一些具有最优块可同步能力的量子可同步码。

关键词: 量子可同步码, 循环码, 对偶包含码, 分圆陪集

Abstract:

A new family of quantum synchronizable codes from generalized cyclotomy of order two over Z2pm are constructed whose synchronization capabilities always reach the upper bound 2pm. In addition, this kind of codes also have ability to correct bit errors and phase errors caused by quantum noise. Finally, some quantum synchronizable codes with optimal capabilities of block synchronization are presented.

Key words: quantum synchronizable codes, cyclic codes, dual-containing codes, cyclotomic cosets

中图分类号: 

  • O236.2

表1

具有最优块同步能力的量子可同步码"

p m n r δ 块同步能力最优的量子可同步码
3 3 54 37 3 [[54+cl+cr, 30]]37
3 4 162 73 3 [[162+cl+cr, 90]]73
11 2 242 23 5 [[242+cl+cr, 198]]23
11 3 2 662 5 55 [[2 662+cl+cr, 2 398]]5
19 1 38 7 3 [[38+cl+cr, 30]]7
19 2 722 11 3 [[722+cl+cr, 570]]11
67 1 134 37 11 [[134+cl+cr, 126]]37
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