New quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$-codes

We use symplectic self-dual additive codes over $ \mathbb{F}_4 obtained from metacirculant graphs to construct, for the first time, \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] qubit with parameters (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $. Secondary constructions applied result in many new that perform better than previous best-known.