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On the minimum weights of 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 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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Authors and Affiliations

  1. Department of Computer Science, Shizuoka University, Hamamatsu, 432–8011, Japan

    Makoto Araya

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

    Masaaki Harada

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  1. Makoto Araya
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  2. Masaaki Harada
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Correspondence to Masaaki Harada.

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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

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