Skip to main content
Top
Published in: Cryptography and Communications 2/2023

22-10-2022

Construction of quaternary Hermitian LCD codes

Author: Keita Ishizuka

Published in: Cryptography and Communications | Issue 2/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We introduce a general construction of many Hermitian LCD [nk] codes from a given Hermitian LCD [nk] code. Furthermore, we present some results on punctured codes and shortened codes of quaternary Hermitian LCD codes. As an application, we improve some of the previously known lower bounds on the largest minimum weights of quaternary Hermitian LCD codes of length \(26 \le n \le 30\).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Araya, M., Harada, M.: On the classification of quaternary optimal Hermitian LCD codes. Cryptogr. Commun. 14(4), 833–847 (2022) MR 4436621 Araya, M., Harada, M.: On the classification of quaternary optimal Hermitian LCD codes. Cryptogr. Commun. 14(4), 833–847 (2022) MR 4436621
2.
go back to reference Araya, M., Harada, M., Saito, K.: Quaternary Hermitian linear complementary dual codes. IEEE Trans. Inform. Theory 66(5), 2751–2759 (2020) MR 4089750 Araya, M., Harada, M., Saito, K.: Quaternary Hermitian linear complementary dual codes. IEEE Trans. Inform. Theory 66(5), 2751–2759 (2020) MR 4089750
3.
go back to reference Bouyuklieva, S.: Optimal binary LCD codes. Des. Codes Cryptogr. 89(11), 2445–2461 (2021) MR 4321779 Bouyuklieva, S.: Optimal binary LCD codes. Des. Codes Cryptogr. 89(11), 2445–2461 (2021) MR 4321779
4.
go back to reference Carlet, C., Guilley, S.: Complementary dual codes for counter-measures to side-channel attacks. Adv. Math. Commun. 10(1), 131–150 (2016) MR 3471065 Carlet, C., Guilley, S.: Complementary dual codes for counter-measures to side-channel attacks. Adv. Math. Commun. 10(1), 131–150 (2016) MR 3471065
5.
go back to reference Carlet, C., Mesnager, S., Tang, C., Qi, Y.: New characterization and parametrization of LCD codes. IEEE Trans. Inform. Theory 65(1), 39–49 (2019) MR 3900976 Carlet, C., Mesnager, S., Tang, C., Qi, Y.: New characterization and parametrization of LCD codes. IEEE Trans. Inform. Theory 65(1), 39–49 (2019) MR 3900976
6.
go back to reference 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. Inform. Theory 64(4, part 2), 3010–3017 (2018) MR 3784604 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. Inform. Theory 64(4, part 2), 3010–3017 (2018) MR 3784604
7.
go back to reference Güneri, C., Özkaya, B., Solé, P.: Quasi-cyclic complementary dual codes. Finite Fields Appl. 42, 67–80 (2016) MR 3550383 Güneri, C., Özkaya, B., Solé, P.: Quasi-cyclic complementary dual codes. Finite Fields Appl. 42, 67–80 (2016) MR 3550383
9.
go back to reference Guenda, K., Jitman, S., Gulliver, T.A.: Constructions of good entanglement-assisted quantum error correcting codes. Des. Codes Cryptogr. 86(1), 121–136 (2018) MR 3742836 Guenda, K., Jitman, S., Gulliver, T.A.: Constructions of good entanglement-assisted quantum error correcting codes. Des. Codes Cryptogr. 86(1), 121–136 (2018) MR 3742836
10.
go back to reference Harada, M.: Existence of new extremal doubly-even codes and extremal singly-even codes. Des. Codes Cryptogr. 8(3), 273–283 (1996) MR 1403866 Harada, M.: Existence of new extremal doubly-even codes and extremal singly-even codes. Des. Codes Cryptogr. 8(3), 273–283 (1996) MR 1403866
11.
go back to reference Harada, M.: Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes. Des. Codes Cryptogr. 89(10), 2295–2312 (2021) MR 4314168 Harada, M.: Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes. Des. Codes Cryptogr. 89(10), 2295–2312 (2021) MR 4314168
12.
go back to reference Harada, M., Saito, K.: Remark on subcodes of linear complementary dual codes. Inform. Process. Lett. 159(160), 105963, 3 (2020) MR 4088439 Harada, M., Saito, K.: Remark on subcodes of linear complementary dual codes. Inform. Process. Lett. 159(160), 105963, 3 (2020) MR 4088439
13.
go back to reference Huffman, W.C., Pless, V.: Fundamentals of error-correcting codes. Cambridge University Press, Cambridge (2003) MR 1996953 Huffman, W.C., Pless, V.: Fundamentals of error-correcting codes. Cambridge University Press, Cambridge (2003) MR 1996953
14.
go back to reference Ishizuka, K.: Classification of optimal quaternary Hermitian LCD codes of dimension 2. J. Algebra Comb. Discrete Struct. Appl. 7(3), 229–236 (2020) MR 4221779 Ishizuka, K.: Classification of optimal quaternary Hermitian LCD codes of dimension 2. J. Algebra Comb. Discrete Struct. Appl. 7(3), 229–236 (2020) MR 4221779
15.
go back to reference Ishizuka, K., Saito, K.: Construction for both self-dual codes and LCD codes. Adv. Math. Commun. (2022) (to appear) Ishizuka, K., Saito, K.: Construction for both self-dual codes and LCD codes. Adv. Math. Commun. (2022) (to appear)
16.
go back to reference Ishizuka, K., Saito, K.: On the existence of quaternary Hermitian LCD codes with H ermitian dual distance 1. Discrete Math. 345(2), Paper No. 112702, 3 (2022) MR 4338405 Ishizuka, K., Saito, K.: On the existence of quaternary Hermitian LCD codes with H ermitian dual distance 1. Discrete Math. 345(2), Paper No. 112702, 3 (2022) MR 4338405
17.
go back to reference Lu, L., Li, R., Guo, L., Fu, Q.: Maximal entanglement entanglement-assisted quantum codes constructed from linear codes. Quantum Inf. Process. 14(1), 165–182 (2015) MR 3296312 Lu, L., Li, R., Guo, L., Fu, Q.: Maximal entanglement entanglement-assisted quantum codes constructed from linear codes. Quantum Inf. Process. 14(1), 165–182 (2015) MR 3296312
18.
go back to reference Lu, L., Zhan, X., Yang, S., Cao, H.: Optimal quaternary Hermitian LCD codes. (2020) arXiv:2010.10166 Lu, L., Zhan, X., Yang, S., Cao, H.: Optimal quaternary Hermitian LCD codes. (2020) arXiv:2010.10166
19.
go back to reference MacWilliams, F.J. Odlyzko, A.M. Sloane, N.J.A. Ward, H.N. Self-dual codes over GF(4). J. Combin. Theory Ser. A 25(3), 288–318 (1978) MR 514624 MacWilliams, F.J. Odlyzko, A.M. Sloane, N.J.A. Ward, H.N. Self-dual codes over GF(4). J. Combin. Theory Ser. A 25(3), 288–318 (1978) MR 514624
20.
go back to reference Massey, J.L.:Linear codes with complementary duals. Discrete Math. 106/107, 337–342 (1992) MR 1181930 Massey, J.L.:Linear codes with complementary duals. Discrete Math. 106/107, 337–342 (1992) MR 1181930
21.
go back to reference Sok, L.: On Hermitian LCD codes and their Gray image. 62, 101623, 20 (2020) MR 4038250 Sok, L.: On Hermitian LCD codes and their Gray image. 62, 101623, 20 (2020) MR 4038250
22.
go back to reference Zhan, X., Li, R., Lu, L., Li, H.: Quatemary Hermitian linear complementary dual codes with small distance. In: 2020 International Conference on Information Science and Education (ICISE-IE). pp. 38–41 (2020) Zhan, X., Li, R., Lu, L., Li, H.: Quatemary Hermitian linear complementary dual codes with small distance. In: 2020 International Conference on Information Science and Education (ICISE-IE). pp. 38–41 (2020)
Metadata
Title
Construction of quaternary Hermitian LCD codes
Author
Keita Ishizuka
Publication date
22-10-2022
Publisher
Springer US
Published in
Cryptography and Communications / Issue 2/2023
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-022-00614-2

Other articles of this Issue 2/2023

Cryptography and Communications 2/2023 Go to the issue

Premium Partner