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Quantum Codes from the Cyclic Codes Over \(\mathbb {F}_{p}[v,w]/\langle v^{2}-1,w^{2}-1,vw-wv\rangle \)

  • Habibul IslamEmail author
  • Om Prakash
  • Ram Krishna Verma
Conference paper
  • 48 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 307)

Abstract

In this article, for any odd prime p, we study the cyclic codes over the finite ring \(R=\mathbb {F}_{p}[v,w]/\langle v^{2}-1,w^{2}-1,vw-wv\rangle \) to obtain the quantum codes over \(\mathbb {F}_{p}\). We obtain the necessary and sufficient condition for cyclic codes which contain their duals and as an application, some new quantum codes are presented at the end of the article.

Keywords

Cyclic code Quantum code Self-orthogonal code Gray map. 

2010 MSC

94B15 94B05 94B60. 

Notes

Acknowledgements

The authors are thankful to the University Grants Commission (UGC) and the Council of Scientific & Industrial Research (CSIR), Govt. of India for financial supports and the Indian Institute of Technology Patna for providing research facilities. Further, the authors would like to thank the anonymous referee(s) for their valuable comments to improve the presentation of the article.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology PatnaPatnaIndia

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