The transversal diagonal Clifford gates of any qubit stabilizer code are exactly one of six matrix groups, determined by the code's endomorphism algebra.
Gottesman.Stabilizer codes and quantum error correction
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A Classification of Transversal Clifford Gates for Qubit Stabilizer Codes
The transversal diagonal Clifford gates of any qubit stabilizer code are exactly one of six matrix groups, determined by the code's endomorphism algebra.