International Journal of Theoretical Physics

, Volume 54, Issue 1, pp 92–99 | Cite as

Constructions of New Nonbinary Quantum Codes



Two new families of good nonbinary quantum codes are constructed in this paper. The first one can be regarded as a generalization of [Theorem 3.2, X. Kai, S. Zhu and Y. Tang, Phys. Rev. A 88, 012326 (2013)], in the sense that we drop the constraint q≡1 (mod 4). The later one is a quantum maximal-distance-separable (MDS) code. Compared the parameters of our quantum MDS codes with the parameters of quantum MDS codes available in the literature, the quantum MDS codes exhibited here have bigger minimum distance.


Quantum codes Quantum MDS codes Cyclotomic cosets Constacyclic codes 



The authors would like to thank the referees for a very meticulous reading of this manuscript. The second author is supported by NSFC (Grant No. 11171370), the Youth Backbone Teacher Foundation of Henan’s University (Grant No. 2013GGJS-152), and Science and Technology Development Program of Henan Province in 2014 (144300510051). The research of the third author is partially supported by NSFC (Grant No. 11271005) and Nanyang Technological University’s research grant number M4080456.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.School of Mathematical SciencesLuoyang Normal UniversityLuoyang, HenanChina
  3. 3.Division of Mathematical SciencesSchool of Physical & Mathematical Sciences, Nanyang Technological UniversitySingaporeSingapore

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