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Quantum codes from Hermitian dual-containing constacyclic codes over \({\mathbb {F}}_{q^{2}}+{v}{\mathbb {F}}_{q^{2}}\)

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Abstract

Let \({\mathbb {R}}\) be the finite non-chain ring \({\mathbb {F}}_{{ q}^{2}}+{v}{\mathbb {F}}_{{ q}^{2}}\), where \({v}^{2}={v}\) and q is an odd prime power. In this paper, we study quantum codes over \({\mathbb {F}}_{{ q}}\) from constacyclic codes over \({\mathbb {R}}\). We define a class of Gray maps, which preserves the Hermitian dual-containing property of linear codes from \({\mathbb {R}}\) to \({\mathbb {F}}_{{ q}^{2}}\). We study \({\alpha }(1-2v)\)-constacyclic codes over \({\mathbb {R}}\), and show that the images of \(\alpha (1-2v)\)-constacyclic codes over \({\mathbb {R}}\) under the special Gray map are \(\alpha ^{2}\)-constacyclic codes over \({\mathbb {F}}_{{ q}^{2}}\). Some new non-binary quantum codes are obtained via the Gray map and the Hermitian construction from Hermitian dual-containing \(\alpha (1-2v)\)-constacyclic codes over \({\mathbb {R}}\).

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Authors and Affiliations

  1. School of Artificial Intelligence and Big Data, Hefei University, Hefei, 230601, Anhui, People’s Republic of China

    Yu Wang

  2. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Xiaoshan Kai, Zhonghua Sun & Shixin Zhu

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  1. Yu Wang
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  2. Xiaoshan Kai
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  3. Zhonghua Sun
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  4. Shixin Zhu
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Correspondence to Yu Wang.

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This work is supported by the National Natural Science Foundation of China (Grant Nos. 61772168, 61972126, 62002093), and the Talent Scientific Research Fund of Hefei University (Grant No.18-19RC61)

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Wang, Y., Kai, X., Sun, Z. et al. Quantum codes from Hermitian dual-containing constacyclic codes over \({\mathbb {F}}_{q^{2}}+{v}{\mathbb {F}}_{q^{2}}\). Quantum Inf Process 20, 122 (2021). https://doi.org/10.1007/s11128-021-03052-w

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