Can classical and quantum information share the same error-correcting code?

By combining projective representation theory with operator algebra error correction, this work builds 'hybrid Clifford codes' that protect classical and quantum information within a single code structure. The approach generalizes quantum stabilizer codes in two directions at once — handling mixed classical-quantum data and a broader class of symmetry representations. The payoff is a unified theorem guaranteeing error correction across all these code types, including exotic non-stabilizer examples.