Abstract
In this paper we construct quantum codes over \(\mathbb F_p\) by using cyclic and \(\lambda \)-cyclic codes over the ring \(R=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^2\mathbb {F}_{p}+v\mathbb {F}_{p} +uv\mathbb {F}_{p}+u^2v\mathbb {F}_{p}+v^2\mathbb {F}_{p}+uv^2\mathbb {F}_{p} +u^2v^2\mathbb {F}_{p}\) where \(v^3=v , u^3=u , uv=vu\) and p is an odd prime integer. Using the idempotent decomposition method, we have given the parameters of the quantum code. Moreover, the structure of cyclic and \(\lambda \)-constacyclic codes over R is studied. Some quantum codes over \(\mathbb {F}_p\) are given.
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Acknowledgements
The authors would like to thank Abdullah Dertli and Yasemin Cengellenmis for their useful suggestions and comments. The authours would also like to thank the anonymous reviewers for their considerable suggestions.
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Gowdhaman, K., Mohan, C., Chinnapillai, D. et al. Construction of quantum codes from \(\lambda \)-constacyclic codes over the ring \(\frac{\mathbb {F}_p[u,v]}{\langle v^3-v , u^3-u , uv-vu\rangle }\). J. Appl. Math. Comput. 65, 611–622 (2021). https://doi.org/10.1007/s12190-020-01407-7
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DOI: https://doi.org/10.1007/s12190-020-01407-7