两个非对称图量子MDS码的构造

doi:10.3778/j.issn.1002-8331.1702-0058

计算机工程与应用 ›› 2017, Vol. 53 ›› Issue (19): 61-64.DOI: 10.3778/j.issn.1002-8331.1702-0058

两个非对称图量子MDS码的构造

程茜1，于慧2

1.青海师范大学数学系，西宁 810008
2.大连交通大学数理系，辽宁大连 116028

出版日期:2017-10-01 发布日期:2017-10-13

Construction of two asymmetric graph quantum MDS codes

CHENG Qian1, YU Hui2

1.Department of Mathematics, Qinghai Normal University, Xining 810008, China
2.Department of Mathematics & Physics, Dalian Jiaotong University, Dalian, Liaoning 116028, China

Online:2017-10-01 Published:2017-10-13

摘要/Abstract

摘要： 量子纠错编码技术在量子信息理论中一直以来有着重要的地位，在量子纠错编码方案中，Schingemann和Werner两人提出了通过构造具有某些性质的图（矩阵）来构造非二元量子码的方法，他们利用这种图论方法构造出很多好的量子码，特别给出量子码[[[5,1,3]]p][(p≥3)]存在性的一个新证明。此方法可从对称量子码推广至非对称量子码的构造，利用推广方法证明了非对称图量子MDS码[[[5,1,4/2]]p]，[(p>5)]和[[[7,1,6/2]]p][(p>7)]的存在性。

关键词: 非对称量子码, 量子MDS码, 图构造

Abstract: Quantum error correction plays a crucial role in quantum information theory. Schlingemann and Werner presented a new way to construct quantum stabilizer codes by finding certain graphs（or matrices）with specific properties, and they constructed several new nonbinary quantum codes by the way, in particular, they gave a new proof on existence of quantum codes[[[5,1,3]]p][(p≥3)]. The way can be generalized the construction of symmetric quantum codes to the asymmetric case. Using this method, the existence of asymmetric graph quantum MDS codes with parameters[[[5,1,4/2]]p] and [[[7,1,6/2]]p]is showed separately for all primes[p>5]and[p>7]by graph machinery.

Key words: asymmetric quantum codes, quantum MDS codes, graph construction

程茜1，于慧2. 两个非对称图量子MDS码的构造[J]. 计算机工程与应用, 2017, 53(19): 61-64.

CHENG Qian1, YU Hui2. Construction of two asymmetric graph quantum MDS codes[J]. Computer Engineering and Applications, 2017, 53(19): 61-64.

两个非对称图量子MDS码的构造

Construction of two asymmetric graph quantum MDS codes

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