JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 161-166.doi: 10.6040/j.issn.1671-9352.0.2022.351

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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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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

CLC Number: 

  • O236.2

Table 1

Some quantum synchronizable codes with optimal capabilities of block synchronization"

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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