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Binary linear complementary dual codes

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Abstract

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual [n, k] codes with the largest minimum weight among all binary linear complementary dual [n, k] codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete classification of binary linear complementary dual [n, k] codes with the largest minimum weight is also given for 1 ≤ k ≤ n ≤ 16.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 15H03633. The authors would like to thank Makoto Araya for his useful discussions. The authors would also like to thank Yuta Watanabe and the anonymous referees for helpful comments.

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  1. Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, 980–8579, Japan

    Masaaki Harada & Ken Saito

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  1. Masaaki Harada
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  2. Ken Saito
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Correspondence to Masaaki Harada.

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Dedicated to Professor Masahiko Miyamoto on His 65th Birthday

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Harada, M., Saito, K. Binary linear complementary dual codes. Cryptogr. Commun. 11, 677–696 (2019). https://doi.org/10.1007/s12095-018-0319-0

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  • DOI: https://doi.org/10.1007/s12095-018-0319-0

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