A Varshamov-Gilbert bound for a class of formally self-dual codes and related quantum codes
It is proved that a class of q-ary (2n, n) formally self-dual codes obtained from symmetric matrices over GF (q), contains codes that meet the Varshamov-Gilbert bound. The codes are self-dual with respect to the symplectic inner product and yield quantum codes encoding one state with n q-ary qubits and having minimum distance proportional to n.
varshamov-gilbert bound self-dual code quantum code