Abstract
Linear complementary dual codes (shortly LCD codes) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1992. Nowadays, LCD codes are extensively studied in the literature and widely applied in data storage, cryptography, etc. In this paper, we prove some properties of binary LCD codes using their shortened and punctured codes. We also present some inequalities for the largest minimum weight \(d_{LCD}(n,k)\) of binary LCD [n, k] codes for given length n and dimension k. Furthermore, we give two tables with the values of \(d_{LCD}(n,k)\) for \(k\le 32\) and \(n\le 40\), and two tables with classification results.
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Acknowledgements
I would like to thank Petar Boyvalenkov for focusing my attention to LCD codes and introducing me to the main literature related to this type of codes. I am also grateful to Iliya Bouyukliev for the included restriction about LCD codes in his program Generation.
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Communicated by V. D. Tonchev.
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This research was supported in part by Bulgarian NSF contract KP-06-N32/2-2019.
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Bouyuklieva, S. Optimal binary LCD codes. Des. Codes Cryptogr. 89, 2445–2461 (2021). https://doi.org/10.1007/s10623-021-00929-w
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DOI: https://doi.org/10.1007/s10623-021-00929-w