[1]邢美菊,陈汉武,张金华,等.有限域上的一类量子码[J].东南大学学报(自然科学版),2010,40(2):282-284.[doi:10.3969/j.issn.1001-0505.2010.02.012]
 Xing Meiju,Chen Hanwu,Zhang Jinhua,et al.A class of quantum codes over finite fields[J].Journal of Southeast University (Natural Science Edition),2010,40(2):282-284.[doi:10.3969/j.issn.1001-0505.2010.02.012]
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有限域上的一类量子码()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
40
期数:
2010年第2期
页码:
282-284
栏目:
计算机科学与工程
出版日期:
2010-03-20

文章信息/Info

Title:
A class of quantum codes over finite fields
作者:
邢美菊 陈汉武 张金华 肖芳英 王烁星
东南大学计算机科学与工程学院, 南京 210096
Author(s):
Xing Meiju Chen Hanwu Zhang Jinhua Xiao Fangying Wang Shuoxing
School of Computer Science and Engineering, Southeast University, Nanjing 210096, China
关键词:
纯量子码 内积 Hermitian内积 校验位
Keywords:
pure quantum code inner product Hermitian inner product check bit
分类号:
TP301.6
DOI:
10.3969/j.issn.1001-0505.2010.02.012
摘要:
在Avanti Ketkar等工作的基础上,进一步研究给出了有限域上的另一类类似BCH码的经典码,并证明与该经典码相对应的[[N,K,D]]q量子码和[[N+1,K-1,D+1]]q(q≥2)扩展量子码都存在.在二元域上构造扩展量子码的过程主要采用了偶校验,其运算在内积上进行; 在非二元域上构造扩展量子码的过程主要采用了使得行向量各个元素相加为0的方法,并借助了有限域上本原元的性质,其运算在Hermitian内积上进行.研究结论扩展了利用经典码构建量子码的范围,证明了扩展量子码的最小距离为D+1,并给出了有关经典非二元码校验位的构造及其相关纯量子码存在的构造性证明方法.分析表明,[[N+1,K-1,D+1]]q扩展量子码比[[N,K,D]]q量子码更适宜于信息的传递.
Abstract:
Based on the work of Avanti Ketkar et al., a class of classical codes similar to BCH codes over finite fields is given, and the existence of both corresponding quantum codes [[N,K,D]]q and extended quantum codes [[N+1,K-1,D+1]]q(q≥2) of those classical codes is proved. On the binary field, the construction process of extended quantum codes mainly uses parity check, and the operation is carried out on inner product. On the nonbinary field, the sum of every element of the vector is set to 0 in the construction process of extended quantum codes, the character of primitive element is used in the construction and the operation is carried out on Hermitian inner product. Research results expend the range of the construction of quantum codes using classical codes and prove that the minimum distance of extended quantum codes is equal to D+1. The construction of check bits of classical nonbinary codes and the constructive proof of existence of related pure quantum codes are given. Analyses show that extended quantum codes [[N+1,K-1,D+1]]q are more suitable for transmitting message than quantum codes [[N,K,D]]q.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 邢美菊(1982—),女,硕士生; 陈汉武(联系人),男,博士,教授,博士生导师,hw-chen@seu.edu.cn.
基金项目: 国家自然科学基金资助项目(60572071,60873101)、江苏省自然科学基金资助项目(BM2006504,BK2007104).
引文格式: 邢美菊,陈汉武,张金华,等.有限域上的一类量子码[J].东南大学学报:自然科学版,2010,40(2):282-284. [doi:10.3969/j.issn.1001-0505.2010.02.012]
更新日期/Last Update: 2010-03-20