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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 4/2021

19-01-2021

Characterization and classification of optimal LCD codes

Authors: Makoto Araya, Masaaki Harada, Ken Saito

Published in: Designs, Codes and Cryptography | Issue 4/2021

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Abstract

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over \(\mathbb {F}_q\) having large minimum weights for \(q \in \{2,3\}\). Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over \(\mathbb {F}_q\), where \((q,k) \in \{(2,4), (3,2),(3,3)\}\). Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over \(\mathbb {F}_q\), where \((q,k) \in \{(2,3), (2,4), (3,2),(3,3)\}\).
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Literature
1.
Araya M., Harada M.: On the classification of linear complementary dual codes. Discret. Math. 342, 270–278 (2019).MathSciNetCrossRef
2.
Araya M., Harada M.: On the minimum weights of binary linear complementary dual codes. Cryptogr. Commun. 12, 285–300 (2020).MathSciNetCrossRef
3.
Araya M., Harada M., Saito K.: Quaternary Hermitian linear complementary dual codes. IEEE Trans. Inf. Theory 66, 2751–2759 (2020).MathSciNetCrossRef
4.
Bonisoli A.: Every equidistant linear code is a sequence of dual Hamming codes. Ars Combin. 18, 181–186 (1984).MathSciNetMATH
5.
Bosma W., Cannon J., Playoust C.: The Magma algebra system I: the user language. J. Symb. Comput. 24, 235–265 (1997).MathSciNetCrossRef
6.
Cameron P.J., van Lint J.H.: Designs, Codes and Their Links. Cambridge University Press, Cambridge (1991).CrossRef
7.
Carlet C., Guilley S.: Complementary dual codes for counter-measures to side-channel attacks. Adv. Math. Commun. 10, 131–150 (2016).MathSciNetCrossRef
8.
Carlet C., Mesnager S., Tang C., Qi Y.: New characterization and parametrization of LCD codes. IEEE Trans. Inf. Theory 65, 39–49 (2019).MathSciNetCrossRef
9.
Carlet C., Mesnager S., Tang C., Qi Y., Pellikaan R.: Linear codes over \(\mathbb{F}_q\) are equivalent to LCD codes for \(q > 3\). IEEE Trans. Inf. Theory 64, 3010–3017 (2018).
10.
Fu Q., Li R., Fu F., Rao Y.: On the construction of binary optimal LCD codes with short length. Int. J. Found. Comput. Sci. 30, 1237–1245 (2019).MathSciNetCrossRef
11.
Galvez L., Kim J.-L., Lee N., Roe Y.G., Won B.-S.: Some bounds on binary LCD codes. Cryptogr. Commun. 10, 719–728 (2018).MathSciNetCrossRef
12.
13.
Harada M., Saito K.: Remark on subcodes of linear complementary dual codes. Inf. Process. Lett. 159, 10596 (2020).MathSciNetMATH
14.
Huffman W.C., Pless V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003).CrossRef
15.
Lina Jr. E.R., Nocon E.G.: On the construction of some LCD codes over finite fields. Manila J. Sci. 9, 67–82 (2016).
16.
Lu L., Li R., Guo L., Fu Q.: Maximal entanglement entanglement-assisted quantum codes constructed from linear codes. Quant. Inf. Process. 14, 165–182 (2015).MathSciNetCrossRef
17.
18.
Massey J.L.: Linear codes with complementary duals. Discret. Math. 106/107, 337–342 (1992).
19.
20.
21.
Metadata
Title
Characterization and classification of optimal LCD codes
Authors
Makoto Araya
Masaaki Harada
Ken Saito
Publication date
19-01-2021
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 4/2021
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-020-00834-8

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