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In group-element index notation, the 1 x 2 base matrices are A = [[{0,28}, {11,19}]] and B = [[{0,51}, {32,109}]]. Checks use H_X = [L(A \u2297 I_2) | R(I_1 \u2297 B*)] and H_Z = [R(I_2 \u2297 B) | L(A* \u2297 I_1)], with * denoting group-algebra conjugate transpose. The binary lift has n=680, k=163, and maximum check weight 6.", "references": [ "arXiv:2607.28795" ], "date": "2026-08-12", "notes": "CSS code in the unrestricted weight-6 class (maximum check weight 6). Validated weight-4 X and Z logical witnesses establish d <= 4; the distance is a witness-backed upper bound, not exact. Relative to [[700,85,3]], it uses 20 fewer physical qubits, encodes 78 more logical qubits, and raises d from 3 to 4, with maximum check weight 6 rather than 4.", "model": "Magic State Labs (Custom) v0.1" }, "family": "lifted-product" }