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New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes

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Abstract

In this paper, some families of asymmetric quantum codes and quantum convolutional codes that satisfy the quantum Singleton bound are constructed by utilizing constacyclic codes with length \(n=\frac{q^2+1}{10h}\), where q is an odd prime power with the form \(q=10hm+t\) or \(q=10hm+10h-t\), where m is a positive integer, and both h and t are odd with \(10h=t^2+1\) and \(t\ge 3\). Compared with those codes constructed in the literature, the parameters of these constructed quantum codes in this paper are more general. Moreover, the distance \(d_z\) of optimal asymmetric quantum codes \([[n,k,d_z/d_x]]_{q^2}\) here is larger than most of the ones given in the literature.

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Acknowledgements

The research was supported by the Natural Science Foundation of China (No. 61802064) and the Natural Science Foundation of Fujian Province, China (Nos. 2016J01281, 2016J01278). We are indebted to anonymous reviewers who have made constructive suggestions for the improvement of this manuscript.

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Authors and Affiliations

  1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou, 350002, China

    Jianzhang Chen & Chunhui Feng

  2. State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, 430079, China

    Youqin Chen

  3. Department of Network Engineering, Chengdu University of Information Technology, Chengdu, 610225, China

    Yuanyuan Huang

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  1. Jianzhang Chen
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  2. Youqin Chen
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  3. Yuanyuan Huang
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  4. Chunhui Feng
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Correspondence to Yuanyuan Huang.

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Chen, J., Chen, Y., Huang, Y. et al. New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes. Quantum Inf Process 18, 40 (2019). https://doi.org/10.1007/s11128-018-2156-7

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