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

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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.

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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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Correspondence to Om Prakash.

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Islam, H., Prakash, O. Quantum codes from the cyclic codes over \(\mathbb {F}_{p}[u,v,w]/\langle u^{2}-1,v^{2}-1,w^{2}-1,uv-vu,vw-wv,wu-uw\rangle \). J. Appl. Math. Comput. 60, 625–635 (2019). https://doi.org/10.1007/s12190-018-01230-1

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  • DOI: https://doi.org/10.1007/s12190-018-01230-1

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