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Quantum codes over Fp from cyclic codes over Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉

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Abstract

In this paper, quantum codes over Fp from cyclic codes over the ring Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉, where u2 = 1, v3 = v, uv = vu and p is an odd prime have been studied. We give the structure of cyclic codes over the ring Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉 and obtain quantum codes over Fp using self-orthogonal property of these classes of codes. Moreover, by using decomposing method, the parameters of the associated quantum code have been determined.

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Acknowledgments

The authors are thankful to the anonymous referees for their careful reading of the paper and valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Mohammad Ashraf

  2. Department of Applied Sciences, The NorthCap University, Gurugram, 122017, India

    Ghulam Mohammad

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  1. Mohammad Ashraf
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  2. Ghulam Mohammad
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Correspondence to Ghulam Mohammad.

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Ashraf, M., Mohammad, G. Quantum codes over Fp from cyclic codes over Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉. Cryptogr. Commun. 11, 325–335 (2019). https://doi.org/10.1007/s12095-018-0299-0

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  • DOI: https://doi.org/10.1007/s12095-018-0299-0

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