  There is a bijection between odd prime dimensional qudit pure stabilizer
states modulo invertible scalars and affine Lagrangian subspaces of finite
dimensional symplectic $\mathbb{F}_p$-vector spaces. In the language of the
stabilizer formalism, full rank stabilizer tableaux are exactly the bases for
affine Lagrangian subspaces. This correspondence extends to an isomorphism of
props: the composition of stabilizer circuits corresponds to the relational
composition of affine subspaces spanned by the tableaux, the tensor product
corresponds to the direct sum. In this paper, we extend this correspondence
between stabilizer circuits and tableaux to the mixed setting; regarding
stabilizer codes as affine coisotropic subspaces (again only in odd prime qudit
dimension/for qubit CSS codes). We show that by splitting the projector for a
stabilizer code we recover the error detection protocol and the error
correction protocol with affine classical processing power.
