Abstract
Given a commutative ring R with identity, a matrix \(A\in M_{s\times l}(R)\), and linear codes \(\mathcal {C}_1, \dots , \mathcal {C}_s\) over R of the same length, this article considers the hull of the matrix-product code \([\mathcal {C}_1 \dots \mathcal {C}_s]\,A\). Consequently, it introduces various sufficient conditions (as well as some necessary conditions in certain cases) under which \([\mathcal {C}_1 \dots \mathcal {C}_s]\,A\) is a complementary dual (LCD) code. As an application, LCD matrix-product codes arising from torsion codes over finite chain rings are considered. Moreover, we show the existence of asymptotically good sequences of LCD matrix-product codes over such rings.
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Acknowledgements
The authors deeply thank the anonymous referees for the careful review and very useful comments which helped in improving the paper. A. Deajim and M. Bouye would like to express their gratitude to King Khalid University for providing administrative and technical support.
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Deajim, A., Bouye, M. & Guenda, K. The hulls of matrix-product codes over commutative rings and applications. J. Appl. Math. Comput. 66, 493–506 (2021). https://doi.org/10.1007/s12190-020-01447-z
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DOI: https://doi.org/10.1007/s12190-020-01447-z