Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (19): 61-64.DOI: 10.3778/j.issn.1002-8331.1702-0058

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Construction of two asymmetric graph quantum MDS codes

CHENG Qian1, YU Hui2   

  1. 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

两个非对称图量子MDS码的构造

程  茜1,于  慧2   

  1. 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

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

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