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.
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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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Islam, H., Prakash, O., Verma, R.K. (2020). Quantum Codes from the Cyclic Codes Over \(\mathbb {F}_{p}[v,w]/\langle v^{2}-1,w^{2}-1,vw-wv\rangle \). In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 307. Springer, Singapore. https://doi.org/10.1007/978-981-15-1157-8_6
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DOI: https://doi.org/10.1007/978-981-15-1157-8_6
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