Some optimal entanglement-assisted quantum codes constructed from quaternary Hermitian linear complementary dual codes

We establish the existence of optimal maximal entanglement entanglement-assisted quantum $[[n,k,d;n-k]{]}_2$ codes for $(n,k,d)=(14,6,7)$, $(15,7,7)$, $(17,6,9)$, $(17,7,8)$, $(19,7,9)$ and $(20,7,10)$. These codes are obtained from quaternary Hermitian linear complementary dual codes. We also give some observation on the largest minimum weights.