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New QEC and EAQEC codes from repeated-root cyclic codes of length \(10p^s\) over finite fields \(\mathbb {F}_{p^m}\)

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Abstract

Let p be an odd prime with \(p\ne 5\). In this paper, we first provide the structures of repeated-root cyclic codes of length \(10p^s\) over finite fields \(\mathbb {F}_{p^m}\). We then give two methods of constructing good quantum error-correcting (QEC) codes from repeated-root cyclic codes of length \(10p^s\) over finite fields \(\mathbb {F}_{p^m}\). By means of the dimensions of repeated-root cyclic codes of length \(10p^s\) over finite fields \(\mathbb {F}_{p^m}\), we exhibit an effective manner for constructing new EAQEC codes. We show that the usage of these methods brings us many good QEC and EQAEC codes having these advantages: (1) the parameters of our QEC and EQAEC codes are different from all the previous constructions; (2) for repeated-root cyclic codes, our methods allows for easily calculating the dimensions of QEC and EQAEC codes, and the numbers c of pre-shared maximally entangled states of EAQEC codes.

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Acknowledgements

The authors would like to sincerely thank the editor and the referees for very meticulous readings of this paper and for valuable suggestions which help us to create an improved version. X. Liu was supported by Research Funds of Hubei Province (Grant No. D20144401 and Q20174503) and Research Project of Hubei Polytechnic University (Grant No. numbers 17xjz03A ).

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Authors and Affiliations

  1. School of Science and Technology, College of Arts and Science of Hubei Normal University, Huangshi, 435109, Hubei, China

    Xiusheng Liu

  2. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, Hubei, China

    Peng Hu

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  1. Xiusheng Liu
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XL and PH discussed and came up with the initial idea. XL developed the theory and edited the text. PH supervised the findings of this work. All authors provided critical feedback and helped shape the research, analysis and manuscript.

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Correspondence to Peng Hu.

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Liu, X., Hu, P. New QEC and EAQEC codes from repeated-root cyclic codes of length \(10p^s\) over finite fields \(\mathbb {F}_{p^m}\). Quantum Inf Process 23, 164 (2024). https://doi.org/10.1007/s11128-024-04374-1

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