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Applicable Algebra in Engineering, Communication and Computing
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05-10-2021 | Original Paper

LCD codes from equitable partitions of association schemes

Author: Andrea Švob

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2023

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Abstract

Linear codes with complementary duals (shortly named LCD codes) are linear codes whose intersection with their duals are trivial. In this paper, we give a method of constructing these type of linear codes from equitable partitions of association schemes. The LCD codes constructed in this paper are of length 2n and dimension n and have the property of being formally self-dual. To illustrate the method we construct LCD codes from some distance-regular graphs.
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Literature
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Carlet, C., Guilley, S.: Complementary dual codes for counter-measures to side-channel attacks. Adv. Math. Commun. 10, 131–150 (2016)MathSciNetCrossRefMATH
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Carlet, C., Mesnager, S., Tang, C., Qi, Y.: Linear codes over \(F_q\) which are equivalent to LCD codes for \(q>3\). IEEE Trans. Inform. Theory 64, 3010–3017 (2018)MathSciNetCrossRefMATH
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Crnković, D., Egan, R., Rodrigues, B.G., Švob, A.: LCD codes from weighing matrices. Appl. Algebra Eng. Commun. Comput. 32, 175–189 (2021)MathSciNetCrossRefMATH
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Crnković, D., Rukavina, S., Švob, A.: Self-orthogonal codes from equitable partitions of association schemes, preprint. arXiv:​1903.​01832
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Metadata
Title
LCD codes from equitable partitions of association schemes
Author
Andrea Švob
Publication date
05-10-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 6/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00532-5

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