Abstract
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over \(\mathbb {F}_q\) having large minimum weights for \(q \in \{2,3\}\). Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over \(\mathbb {F}_q\), where \((q,k) \in \{(2,4), (3,2),(3,3)\}\). Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over \(\mathbb {F}_q\), where \((q,k) \in \{(2,3), (2,4), (3,2),(3,3)\}\).
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Acknowledgements
The authors would like to thank Tatsuya Maruta for his useful comments. This work was supported by JSPS KAKENHI Grant Number 19H01802.
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Communicated by T. Helleseth.
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Araya, M., Harada, M. & Saito, K. Characterization and classification of optimal LCD codes. Des. Codes Cryptogr. 89, 617–640 (2021). https://doi.org/10.1007/s10623-020-00834-8
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DOI: https://doi.org/10.1007/s10623-020-00834-8