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Quantum codes from cyclic codes over the mixed alphabet structure

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Abstract

Let p be an odd prime, \(q=p^m\), \(R_1=\mathbb F_{q}+u{\mathbb {F}}_{q}+v{\mathbb {F}}_{q}+uv{\mathbb {F}}_{q}\) with \(u^2=1\), \(v^2=1\), \(uv=vu\) and \(R_2={\mathbb {F}}_{q}[u,v,w]/\langle u^2-1, v^2-1,w^2-1, uv-vu,vw-wv,wu-uw\rangle \) with \(u^2=1\), \(v^2=1\), \(w^2=1\), \(uv=vu\), \(vw=wv\), \(wu=uw\). In this paper, \({\mathbb {F}}_q R_1R_2\)-cyclic codes are introduced. We construct quantum error-correcting codes from \({\mathbb {F}}_q R_1R_2\)-cyclic codes and introduced a Gray map to find new and better quantum error-correcting codes than previously known quantum error-correcting codes over \({\mathbb {F}}_{q}\).

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

The authors are thankful to the anonymous reviewers for their fruitful suggestions.

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Correspondence to Ghulam Mohammad.

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Ashraf, M., Khan, N. & Mohammad, G. Quantum codes from cyclic codes over the mixed alphabet structure. Quantum Inf Process 21, 180 (2022). https://doi.org/10.1007/s11128-022-03491-z

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