On the minimum weights of quaternary Hermitian LCD codes

We study the largest minimum weights among quaternary Hermitian LCD codes. We determine the largest minimum weights among quaternary Hermitian LCD codes of length n and dimension k for \(k \le n \le 17\) $k\le n\le 17$ . A quaternary Hermitian LCD [21, 5, 13] code and a quaternary Hermitian LCD [21, 9, 9] code are also constructed for the first time. An updated table of the largest minimum weights among quaternary Hermitian LCD [n, k] codes is also given for \(k \le n \le 30\) $k\le n\le 30$ .