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量子常数循环码

李卓;邢莉娟;王新梅
  

  1. (西安电子科技大学 综合业务网理论及关键技术国家重点实验室,陕西 西安 710071)
  • 收稿日期:2007-11-12 修回日期:1900-01-01 出版日期:2009-02-20 发布日期:2009-02-10
  • 通讯作者: 李卓

Quantum constacyclic codes

LI Zhuo;XING Li-juan;WANG Xin-mei
  

  1. (State Key Lab. of Integrated Service Networks, Xidian Univ., Xi’an 710071, China)
  • Received:2007-11-12 Revised:1900-01-01 Online:2009-02-20 Published:2009-02-10
  • Contact: LI Zhuo

摘要: 提出了一类新的量子稳定子码的构造方法.寻找量子稳定子码的问题可以转化为寻找GF(4)上迹内积自正交的经典加码的问题.利用这一联系,提出了GF(4)上的经典常数循环码满足迹内积自正交的充要条件,从而构造出了对应的量子常数循环码.最后给出了该类码的一些例子,特别是利用该方法可以构造出量子汉明码.常见的量子循环码实际上是量子常数循环码的一个子类.

关键词: 量子常数循环码, 量子稳定子码, GF(4)上常数循环码, 量子汉明码

Abstract: A new class of quantum stabilizer codes is presented. The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Based on this connection, one method for constructing quantum constacyclic codes is presented by finding self-orthogonal classical constacyclic codes over the field GF(4) under a trace inner product. Finally, some examples are given. As an application of this method, quantum Hamming codes are constructed. This class of quantum codes includes well-known quantum cyclic codes.

Key words: quantum constacyclic codes, stabilizer quantum-error-correcting codes, constacyclic codes over GF(4), quantum Hamming codes

中图分类号: 

  • TN911.2