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Some new quantum codes from constacyclic codes

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Abstract

In this paper, let q be an odd prime power. Based on new constacyclic codes which contain their Hermitian duals and Hermitian construction, we construct some classes of quantum MDS codes and quantum codes. When \(q\equiv 1\ \textrm{mod}\ 4\), x and y are a divisor of \(q-1\) and \(q+1\), respectively, we can construct a class of new quantum codes of length \(n=2xy\frac{q^{2m}-1}{q^2-1}\) for odd \(x,y,m\ge 3\). These codes have larger dimensions than existing codes. In addition, for q with the form \(2am\pm \sqrt{(x^2+y^2)a-1}\) and odd x, y, a with \(gcd(x,y)=1\), we get some quantum MDS codes of length \(n=\frac{q^2+1}{a}\).

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Acknowledgements

This research was funded by the National Natural Science Foundation of China (Grant Number 11971004).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Shanqi Pang, Miaomiao Zhang, Mengqian Chen & Chaomeng Zhang

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  1. Shanqi Pang
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  2. Miaomiao Zhang
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Correspondence to Shanqi Pang.

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Pang, S., Zhang, M., Chen, M. et al. Some new quantum codes from constacyclic codes. Quantum Inf Process 23, 11 (2024). https://doi.org/10.1007/s11128-023-04219-3

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