Abstract
Codes on permutations and multi-permutations have been received much attention due to their potential applications in communications and storage systems. This paper proposes two constructions for balanced multi-permutation codes capable of correcting a single burst of deletions of length t and length up to t, respectively. For any target value of t, the first construction is based on the interleaving of t sub-codes on permutations, whereas the second one is based on the interleaving of \(t+1\) sub-codes on multi-permutations that are arranged in all possible orders using a stabilizer subgroup. The decoding methods are included in proofs and verified by examples. Numerical results show that both constructions can achieve higher code rates than existing ones while maintaining simple interleaving structures.
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Acknowledgements
Hui Han is supported by the National Natural Science Foundation of China (Grant No. 62001362), the Open Fund from the Chongqing Key Lab of Computer Network and Communication Technology (CY-CNCL-2021-01), the China Postdoctoral Science Foundation (Grant No. 2020M683427) and the Fundamental Research Funds for the Central Universities under Grant XJS220310. Jianjun Mu is supported in part by the National Natural Science Foundation of China (Grant No. 61977051). Xiaopeng Jiao is supported in part by the National Natural Science Foundation of China (Grant No. 61971322).
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Communicated by C. J. Colbourn.
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Han, H., Mu, J., Jiao, X. et al. Constructions of multi-permutation codes correcting a single burst of deletions. Des. Codes Cryptogr. 91, 1923–1934 (2023). https://doi.org/10.1007/s10623-023-01190-z
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DOI: https://doi.org/10.1007/s10623-023-01190-z