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Your question can in parts be seen as a notational issue. The notation $[[n,k,d]]_D$ is often (but not always) reserved for codes is of stabilizer type. As the paper by Calderbank et al shows, qubit stabilizer codes are equivalent to additive self-orthogonal GF(4)^n classical codes. This construction generalizes, see Refs. Ketkar et al. and Ashikhmin and ...

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