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

Yıl 2020, Cilt: 7 Sayı: 3, 229 - 236, 06.09.2020

Keita Ishızuka

https://doi.org/10.13069/jacodesmath.790748

Cited By: 2

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 $2$.

Anahtar Kelimeler

Linear complementary dual code, Hermitian linear complementary dual code, Optimal codes

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.