Abstract
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weights d(n,k) among all binary linear complementary dual [n,k] codes. We determine d(n,4) for n ≡ 2,3,4,5,6,9,10,13 (mod 15), and d(n,5) for n ≡ 3,4,5,7,11,19,20, 22,26 (mod 31). Combined with known results, d(n,k) are also determined for n ≤ 24.
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Number 15H03633. In this work, the supercomputer of ACCMS, Kyoto University was partially used. The authors would like to thank the anonymous referees and Editor-in-Chief Claude Carlet for the useful comments.
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Dedicated to Professor Masaaki Kitazume on His 60th Birthday
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Araya, M., Harada, M. On the minimum weights of binary linear complementary dual codes. Cryptogr. Commun. 12, 285–300 (2020). https://doi.org/10.1007/s12095-019-00402-5
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DOI: https://doi.org/10.1007/s12095-019-00402-5