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Quantum Reed–Muller code

A fixed CSS block built by evaluating the four binary coordinate functions on every nonzero point of F_2^4. Those evaluation rows are the X checks; their orthogonal complement after adjoining the all-one logical row supplies the Z checks. The resulting protected qubit corrects one arbitrary single-qubit error and admits a transversal non-Clifford phase, making this block both the switching partner of the Steane code and the algebraic core of 15-to-1 magic-state distillation.