{
 "schema_version": "0.1",
 "name": "[[16,6,4]] quantum Reed-Muller code, single-layer 2D-local layout",
 "code_type": "CSS",
 "n": 16,
 "k": 6,
 "checks": {
  "X": [
   [
    1,
    3,
    5,
    7,
    9,
    11,
    13,
    15
   ],
   [
    0,
    2,
    4,
    6,
    8,
    10,
    12,
    14
   ],
   [
    2,
    3,
    6,
    7,
    10,
    11,
    14,
    15
   ],
   [
    4,
    5,
    6,
    7,
    12,
    13,
    14,
    15
   ],
   [
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15
   ]
  ],
  "Z": [
   [
    1,
    3,
    5,
    7,
    9,
    11,
    13,
    15
   ],
   [
    0,
    2,
    4,
    6,
    8,
    10,
    12,
    14
   ],
   [
    2,
    3,
    6,
    7,
    10,
    11,
    14,
    15
   ],
   [
    4,
    5,
    6,
    7,
    12,
    13,
    14,
    15
   ],
   [
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    1,
    6,
    8,
    15
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    1,
    6,
    8,
    15
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "CSS code from Reed-Muller RM(1,4): H_X = H_Z = the RM(1,4) generator with the all-ones row dropped, which halves the check weight from 16 to 8 while generating the same stabilizer group. The submitted artifact is the LAYOUT: 16 qubits placed in the plane by direct minimization of the maximum check diameter subject to unit minimum site spacing, reaching r = 2.8586.",
  "origin": "submission",
  "date": "2026-07-25",
  "model": "Claude Opus 5",
  "notes": "The CODE is textbook and its parameters are known (Steane 1996 / Reed-Muller CSS constructions); 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 = 2.8586, rho = 1 this scores g = 0.3594 versus 0.0717 for the previous best qLDPC entry on the board. Distance is MILP-certified exact on both sides (verify/certify.py: no logical < 4 exists), filed as upper_bound per board policy. CAVEAT: this radius is NOT converged - independent seeds landed at 2.8586 / 2.8593 / 2.8693 / 2.8773 / 2.8794, so a better layout very likely exists. The per-check packing floor for weight-8 is 2.2470, which would give g = 0.944; the gap is open. RM(1,4) also has basis freedom (its stabilizer in GL(5,2) is only AGL(4,2), giving four basis classes with different check-pair graphs), worth roughly 0.09 of radius and not fully explored.",
  "novelty": "known_parameters",
  "references": [
   "quant-ph/9601029 (Steane, 1996)",
   "errorcorrectionzoo.org/c/quantum_reed_muller"
  ]
 },
 "family": "other",
 "locality": {
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  "layers": 1
 }
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