Binary linear complementary dual codes

Masaaki Harada; Ken Saito

doi:10.1007/s12095-018-0319-0

Binary linear complementary dual codes

Masaaki Harada, Ken Saito

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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.

Original language	English
Pages (from-to)	677-696
Number of pages	20
Journal	Cryptography and Communications
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/s12095-018-0319-0
Publication status	Published - 2019 Jul 15

Keywords

Binary code
K-cover
Linear complementary dual code

ASJC Scopus subject areas

Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s12095-018-0319-0

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title = "Binary linear complementary dual codes",

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.",

keywords = "Binary code, K-cover, Linear complementary dual code",

author = "Masaaki Harada and Ken Saito",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

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day = "15",

doi = "10.1007/s12095-018-0319-0",

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T1 - Binary linear complementary dual codes

AU - Harada, Masaaki

AU - Saito, Ken

N1 - Funding Information: 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. Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2019/7/15

Y1 - 2019/7/15

N2 - 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.

AB - 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.

KW - Binary code

KW - K-cover

KW - Linear complementary dual code

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JO - Cryptography and Communications

JF - Cryptography and Communications

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ER -

Binary linear complementary dual codes

Abstract

Keywords

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