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233, 394 ] } }, "provenance": { "authors": [ "@npdeep" ], "construction": "Generic group lifted-product CSS code over the nonabelian dihedral group D52 of order 52. In group-element index notation, the monomial 2 x 3 base matrices are A = [[{0}, {14}, {43}], [{23}, {13}, {44}]] and B = [[{0}, {14}, {19}], [{12}, {35}, {18}]]. Checks use H_X = [L(A \u2297 I_3) | R(I_2 \u2297 B*)] and H_Z = [R(I_3 \u2297 B) | L(A* \u2297 I_2)], with * denoting group-algebra conjugate transpose. The binary lift has n=676, k=71, and maximum check weight 5.", "references": [ "arXiv:2607.28795" ], "date": "2026-08-12", "notes": "CSS code in the unrestricted weight-6 class (maximum check weight 5). Validated weight-4 X and Z logical witnesses establish d <= 4; the distance is a witness-backed upper bound, not exact. Relative to [[696,76,3]], it uses 20 fewer physical qubits and raises d from 3 to 4, with k=71 rather than 76 and maximum check weight 5 rather than 4.", "model": "Magic State Labs (Custom) v0.1" }, "family": "lifted-product" }