New Qubit Codes from Multidimensional Circulant Graphs
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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 _4 codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths 4≤ n ≤ 40 and show that many optimal ℓ, 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.
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