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Quantum codes from the cyclic codes over \(\mathbb {F}_{p}[u,v,w]/\langle u^{2}-1,v^{2}-1,w^{2}-1,uv-vu,vw-wv,wu-uw\rangle \)

  • Habibul Islam
  • Om PrakashEmail author
Original Research
  • 56 Downloads

Abstract

In this article, for any odd prime p, we construct the quantum codes over \(\mathbb {F}_{p}\) by using the cyclic codes of length n over \(R=\mathbb {F}_{p}[u,v,w]/\langle u^{2}-1,v^{2}-1,w^{2}-1,uv-vu,vw-wv,wu-uw\rangle \). We obtain the self-orthogonal properties of cyclic codes over R and as an application, present some new quantum codes.

Keywords

Cyclic code Quantum code Gray map Self-orthogonal code 

Mathematics Subject Classification

94B05 94B15 94B35 94B60 

Notes

Acknowledgements

The authors are thankful to the University Grants Commission (UGC) for financial support and Indian Institute of Technology Patna for providing research facilities. Also, the authors would like to thank the anonymous referee(s) and the editor for their valuable comments to improve the presentation of the article.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology PatnaPatnaIndia

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