Improved constructions for quantum maximum distance separable codes

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Abstract

In this work, we further improve the distance of the quantum maximum distance separable (MDS) codes of length \(n=\frac{q^2+1}{10}\). This yields new families of quantum MDS codes. We also construct a family of new quantum MDS codes with parameters \([[\frac{q^2-1}{3}, \frac{q^2-1}{3}-2d+2, d]]_{q}\), where \(q=2^m\), \(2\le d\le \frac{q-1}{3}\) if \(3\mid (q+2)\), and \(2\le d\le \frac{2q-1}{3}\) if \(3\mid (q+1)\). Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.

Keywords

Quantum code Cyclic code MDS code 
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Notes

Acknowledgements

We are indebted to the anonymous referees for their valuable comments and suggestions that helped to improve significantly the quality of this paper. This work was supported by the Anhui Provincial Natural Science Foundation (1408085MA05).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsHuizhou UniversityHuizhouPeople’s Republic of China

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