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Classification of optimal quaternary Hermitian LCD codes of dimension $2$

Yıl 2020, Cilt: 7 Sayı: 3, 229 - 236, 06.09.2020
https://doi.org/10.13069/jacodesmath.790748

Öz

Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial.
The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$. Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial.
The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$.

Kaynakça

  • [1] M. Araya, M. Harada, On the classification of linear complementary dual codes, Discrete Math. 342 (2019) 270–278.
  • [2] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997) 235–265.
  • [3] C. Carlet, S. Guilley, Complementary dual codes for counter–measures to side–channel attacks, Adv. Math. Commun. 10 (2016) 131–150.
  • [4] C. Carlet, S. Mesnager, C. Tang, Y. Qi, R. Pellikaan, Linear codes over $F_q$ are equivalent to LCD codes for q > 3, IEEE Trans. Inform. Theory 64 (2018) 3010–3017.
  • [5] C. Güneri, B. Özkaya, P. Solé, Quasi–cyclic complementary dual codes, Finite Fields Appl. 42 (2016) 67–80.
  • [6] L. Lu, R. Li, L. Guo, Q. Fu, Maximal entanglement entanglement–assisted quantum codes constructed from linear codes, Quantum Inf. Process. 14 (2015) 165–182.
  • [7] J. L. Massey, Linear codes with complementary duals, Discrete Math. 106/107 (1992) 337–342.
Yıl 2020, Cilt: 7 Sayı: 3, 229 - 236, 06.09.2020
https://doi.org/10.13069/jacodesmath.790748

Öz

Kaynakça

  • [1] M. Araya, M. Harada, On the classification of linear complementary dual codes, Discrete Math. 342 (2019) 270–278.
  • [2] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997) 235–265.
  • [3] C. Carlet, S. Guilley, Complementary dual codes for counter–measures to side–channel attacks, Adv. Math. Commun. 10 (2016) 131–150.
  • [4] C. Carlet, S. Mesnager, C. Tang, Y. Qi, R. Pellikaan, Linear codes over $F_q$ are equivalent to LCD codes for q > 3, IEEE Trans. Inform. Theory 64 (2018) 3010–3017.
  • [5] C. Güneri, B. Özkaya, P. Solé, Quasi–cyclic complementary dual codes, Finite Fields Appl. 42 (2016) 67–80.
  • [6] L. Lu, R. Li, L. Guo, Q. Fu, Maximal entanglement entanglement–assisted quantum codes constructed from linear codes, Quantum Inf. Process. 14 (2015) 165–182.
  • [7] J. L. Massey, Linear codes with complementary duals, Discrete Math. 106/107 (1992) 337–342.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Keita Ishızuka Bu kişi benim 0000-0001-5943-6245

Yayımlanma Tarihi 6 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 7 Sayı: 3

Kaynak Göster

APA Ishızuka, K. (2020). Classification of optimal quaternary Hermitian LCD codes of dimension $2$. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(3), 229-236. https://doi.org/10.13069/jacodesmath.790748
AMA Ishızuka K. Classification of optimal quaternary Hermitian LCD codes of dimension $2$. Journal of Algebra Combinatorics Discrete Structures and Applications. Eylül 2020;7(3):229-236. doi:10.13069/jacodesmath.790748
Chicago Ishızuka, Keita. “Classification of Optimal Quaternary Hermitian LCD Codes of Dimension $2$”. Journal of Algebra Combinatorics Discrete Structures and Applications 7, sy. 3 (Eylül 2020): 229-36. https://doi.org/10.13069/jacodesmath.790748.
EndNote Ishızuka K (01 Eylül 2020) Classification of optimal quaternary Hermitian LCD codes of dimension $2$. Journal of Algebra Combinatorics Discrete Structures and Applications 7 3 229–236.
IEEE K. Ishızuka, “Classification of optimal quaternary Hermitian LCD codes of dimension $2$”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy. 3, ss. 229–236, 2020, doi: 10.13069/jacodesmath.790748.
ISNAD Ishızuka, Keita. “Classification of Optimal Quaternary Hermitian LCD Codes of Dimension $2$”. Journal of Algebra Combinatorics Discrete Structures and Applications 7/3 (Eylül 2020), 229-236. https://doi.org/10.13069/jacodesmath.790748.
JAMA Ishızuka K. Classification of optimal quaternary Hermitian LCD codes of dimension $2$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7:229–236.
MLA Ishızuka, Keita. “Classification of Optimal Quaternary Hermitian LCD Codes of Dimension $2$”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy. 3, 2020, ss. 229-36, doi:10.13069/jacodesmath.790748.
Vancouver Ishızuka K. Classification of optimal quaternary Hermitian LCD codes of dimension $2$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7(3):229-36.