{
 "schema_version": "0.1",
 "name": "[[15,7,3]] quantum Hamming code, single-layer 2D-local layout",
 "code_type": "CSS",
 "n": 15,
 "k": 7,
 "checks": {
  "X": [
   [
    0,
    2,
    4,
    6,
    8,
    10,
    12,
    14
   ],
   [
    1,
    2,
    5,
    6,
    9,
    10,
    13,
    14
   ],
   [
    3,
    4,
    5,
    6,
    11,
    12,
    13,
    14
   ],
   [
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14
   ]
  ],
  "Z": [
   [
    0,
    2,
    4,
    6,
    8,
    10,
    12,
    14
   ],
   [
    1,
    2,
    5,
    6,
    9,
    10,
    13,
    14
   ],
   [
    3,
    4,
    5,
    6,
    11,
    12,
    13,
    14
   ],
   [
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    6,
    8,
    13
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    6,
    8,
    13
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "CSS quantum Hamming code (Steane construction) from the classical [15,11,3] Hamming code: H_X = H_Z = the 4x15 Hamming parity-check matrix, which is self-orthogonal over GF(2). The submitted artifact is the LAYOUT: 15 qubits placed in the plane by direct minimization of the maximum check diameter subject to unit minimum site spacing, reaching r = sqrt(7) = 2.6458.",
  "origin": "submission",
  "date": "2026-07-25",
  "model": "Claude Opus 5",
  "notes": "The CODE is textbook and its parameters are known (Steane 1996); provenance.novelty is known_parameters. The contribution is the verified single-layer 2D-local LAYOUT, which is what the board's geometric efficiency g = 4kd^2/(n rho^2 r^4) measures. At r = sqrt(7), rho = 1 this scores g = 0.3429 versus 0.0717 for the previous best qLDPC entry on the board, and it is the first native occupant of the weight-8 x local-2d-single cell. The radius appears optimal: the 11 qubits whose Hamming column has weight >= 2 form a core that alone requires sqrt(7), and two independent optimizers converged there. Distance is MILP-certified exact on both sides (verify/certify.py: no logical < 3 exists), though it is filed as upper_bound per board policy. Naive random multistart converges to a false optimum at r = 2.9093; basin hopping seeded from the incumbent is needed to reach sqrt(7).",
  "novelty": "known_parameters",
  "references": [
   "quant-ph/9601029 (Steane, Multiple particle interference and quantum error correction, 1996)",
   "errorcorrectionzoo.org/c/quantum_hamming"
  ]
 },
 "family": "other",
 "locality": {
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  "layers": 1
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