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Hulls of constacyclic codes over finite non-chain rings and their applications in quantum codes construction

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Abstract

We study hulls of constacyclic codes of length n over a finite non-chain ring \({\mathbb {F}}_q+v{\mathbb {F}}_q\) with respect to the Euclidean and Hermitian inner products, where \(v^2=v\). Under a special Gray map from \({\mathbb {F}}_q+v{\mathbb {F}}_q\) to \({\mathbb {F}}^2_q\), dimensions of hulls of Gary images of constacyclic codes are obtained. Some new quantum error-correcting codes (QECCs) with good parameters are constructed by the quantum construction X method under the Euclidean and Hermitian inner products, respectively. Some of these QECCs are MDS with the minimum distance greater than \(\frac{q}{2}\), and a few of these QECCs are MDS with the minimum distance equal to q.

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Data availability

The datasets generated during the current study are not publicly available due to the computational algorithm for searching good quantum error-correcting codes but are available from the corresponding author on reasonable request.

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Acknowledgements

Jian Gao is supported by the Shandong Provincial Natural Science Foundation (No. ZR2022MA024), the National Natural Science Foundation of China (Grant Nos. 12071264, 11701336) and the IC Program of Shandong Institutions of Higher Learning For Youth Innovative Talents. Yun Gao is supported by R &D Program of Beijing Municipal Education Commission(Grant No. KM202310037002) and the Youth Scientific Research Fund of Beijing Wuzi University (Grant No. 2022XJQN25).

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  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, People’s Republic of China

    Zhaoyang Tian & Jian Gao

  2. School of Statistics and Data Science, Beijing Wuzi University, Beijing, 101149, People’s Republic of China

    Yun Gao

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Tian, Z., Gao, J. & Gao, Y. Hulls of constacyclic codes over finite non-chain rings and their applications in quantum codes construction. Quantum Inf Process 23, 9 (2024). https://doi.org/10.1007/s11128-023-04230-8

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