Improved Quantum Codes from Metacirculant Graphs via Self-Dual Additive ${\mathbb{F}}_4$-Codes

Abstract

We use symplectic self-dual additive codes over ${\mathbb{F}}_4$ obtained from metacirculant graphs to construct, for the first time, $[[\ell ,0,d]]$ 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.