On the classification of quaternary optimal Hermitian LCD codes

Abstract

We propose a method for a classification of quaternary Hermitian LCD codes having large minimum weights. By using this method, we complete a classification of quaternary optimal Hermitian LCD codes of dimension 3. We also give an alternative classification of quaternary optimal Hermitian LCD codes of dimension 2 and a classification of quaternary near-optimal Hermitian LCD codes of dimension 2.

Construction for both self-dual codes and LCD codes

“…Galvez, Kim, Lee, Roe and Won [11], Harada and Saito [19], Araya and Harada [1], Araya, Harada and Saito [3] determined the exact value of d LCD (n, k) for k = 2, 3, 4, 5 respectively. Also, Dougherty, Kim, Ozkaya, Sok and Solé [10], Araya and Harada [2], Araya, Harada and Saito [4] determined the exact value of d LCD (n, k) for k = n − 1, k ∈ {n − 2, n − 3, n − 4}, k = n − 5 respectively. For all n = 26, 28 ≤ n ≤ 40, Bouyuklieva [7] determined the exact value of d LCD (n, k) for 5 ≤ k ≤ 8.…”