Research Article
BibTex RIS Cite

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

Year 2020, , 229 - 236, 06.09.2020
https://doi.org/10.13069/jacodesmath.790748

Abstract

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 $2$.

References

  • [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.
Year 2020, , 229 - 236, 06.09.2020
https://doi.org/10.13069/jacodesmath.790748

Abstract

References

  • [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.
There are 7 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Keita Ishızuka This is me 0000-0001-5943-6245

Publication Date September 6, 2020
Published in Issue Year 2020

Cite

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. September 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, no. 3 (September 2020): 229-36. https://doi.org/10.13069/jacodesmath.790748.
EndNote Ishızuka K (September 1, 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, vol. 7, no. 3, pp. 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 (September 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, vol. 7, no. 3, 2020, pp. 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.