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l-LCP of codes and their applications to EAQEC codes

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Abstract

In this paper, we first generalize the complementary pair of codes over finite fields to an l-linear complementary pair (l-LCP) of codes. Then two criteria of l-LCP of codes over finite fields are obtained. We especially investigate l-LCP of constacyclic codes. When C and D are all \(\lambda \)-constacyclic codes, we obtain a characterization of (C, D) to be l-LCP of codes. When C and D are cyclic and negacyclic codes, we give a sufficient condition of (C, D) to be l-LCP of codes. As an application, by means of the l-LCP of codes over finite fields, we exhibit two methods of constructing entanglement-assisted quantum error correcting (EAQEC) codes. Notably, the parameters of our EAQEC codes are new and flexible.

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Data sharing not applicable to this article as no data sets were generated or analysed during the current study.

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Acknowledgements

This work was supported by Research Funds of Hubei Province (Grant No. Q20164505) and the talent project of Hubei Polytechnic University of China (Grant No. 16xjzo8R).

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Authors and Affiliations

  1. School of Medicin, Hubei Polytechnic University, Huangshi, 435003, Hubei, China

    Jie Liu

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

    Xiusheng Liu

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  1. Jie Liu
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Correspondence to Xiusheng Liu.

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Liu, J., Liu, X. l-LCP of codes and their applications to EAQEC codes. Quantum Inf Process 22, 186 (2023). https://doi.org/10.1007/s11128-023-03932-3

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