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A class of negacyclic BCH codes and its application to quantum codes

  • Shixin Zhu
  • Zhonghua Sun
  • Ping Li
Article
  • 148 Downloads

Abstract

In this paper, we study negacyclic BCH codes over \(\mathbb {F}_{q}\) of length \(n=(q^{2m}-1)/(q-1)\), where q is an odd prime power and m is a positive integer. In particular, the dimension, the minimum distance and the weight distribution of some negacyclic BCH codes over \(\mathbb {F}_{q}\) of length \(n=(q^{2m}-1)/(q-1)\) are determined. Two classes of negacyclic BCH codes meeting the Griesmer bound are obtained. As an application, we construct quantum codes with good parameters from this class of negacyclic BCH codes.

Keywords

Negacyclic code BCH code Quantum code Cyclotomic coset 

Mathematics Subject Classification

94B05 94B50 

Notes

Acknowledgements

The authors would like to thank the anonymous referees who gave many helpful comments and suggestions to greatly improve the presentation of the paper. The research was supported in part by the National Natural Science Foundation of China under Grant Nos. 61772168, 61572168 and 11501156.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of MathematicsHefei University of TechnologyHefeiChina

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