Two new qubit stabilizer codes with parameters [77,0,19]2​ and [90,0,22]2​ are constructed for the first time by employing additive symplectic
self-dual \F_4 codes from multidimensional circulant (MDC) graphs. We
completely classify MDC graph codes for lengths 4≤n≤40 and show that
many optimal \dsb{\ell, 0, d} qubit codes can be obtained from the MDC
construction. Moreover, we prove that adjacency matrices of MDC graphs have
nested block circulant structure and determine isomorphism properties of MDC
graphs