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Linear ℓ-intersection pairs of MDS codes and their applications to AEAQECCs

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Abstract

Two linear codes are said to be a linear ℓ-intersection pair if their intersection has dimension ℓ. Guenda et al. (Des Codes Cryptogr. 88, 133–152, 2020) constructed most of the linear ℓ-intersection pairs of MDS codes and we complement their results by constructing some linear ℓ-intersection pairs of MDS codes over \(\mathbb {F}_{q}\) of lengths n = q,q + 1. Furthermore, we construct all the possible linear ℓ-intersection pairs of MDS codes over \(\mathbb {F}_{2^{m}}\) of length n = 2m + 2 ≥ 6. As a consequence, linear ℓ-intersection pairs of MDS codes for all possible parameters are given. Moveover, we can apply our results to asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) and obtain all the possible pure MDS CSS-type AEAQECCs.

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Acknowledgements

The research of Z. Huang, W. Fang and F.-W. Fu is supported in part by the National Key Research and Development Program of China (Grant Nos. 2018YFA0704703 and 2021YFA1001000), the National Natural Science Foundation of China (Grant No. 61971243), the Natural Science Foundation of Tianjin (20JCZDJC00610), the Fundamental Research Funds for the Central Universities of China (Nankai University).

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Authors and Affiliations

  1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Ziteng Huang

  2. School of Cyber Science and Technology, Shandong University, Qingdao, 266237, China

    Weijun Fang

  3. Chern Institute of Mathematics and LPMC, and Tianjin Key Laboratory of Network and Data Security Technology, Nankai University, Tianjin, 300071, China

    Fang-Wei Fu

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  1. Ziteng Huang
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  2. Weijun Fang
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Correspondence to Weijun Fang.

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Huang, Z., Fang, W. & Fu, FW. Linear ℓ-intersection pairs of MDS codes and their applications to AEAQECCs. Cryptogr. Commun. 14, 1189–1206 (2022). https://doi.org/10.1007/s12095-022-00582-7

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