Improved 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, $[[\mathrm{\ell },0,d]]$ qubit codes with parameters $(\ell,d) \in {(78, 20), (90, 21), (91, 22), (93,21),(96,21)}$. Secondary constructions applied to the qubit codes result in many qubit codes that perform better than the previous best-known.