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

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 $2$.

Keywords

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

References

1. [1] M. Araya, M. Harada, On the classification of linear complementary dual codes, Discrete Math. 342 (2019) 270–278.
2. [2] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997) 235–265.
3. [3] C. Carlet, S. Guilley, Complementary dual codes for counter–measures to side–channel attacks, Adv. Math. Commun. 10 (2016) 131–150.
4. [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. [5] C. Güneri, B. Özkaya, P. Solé, Quasi–cyclic complementary dual codes, Finite Fields Appl. 42 (2016) 67–80.
6. [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. [7] J. L. Massey, Linear codes with complementary duals, Discrete Math. 106/107 (1992) 337–342.