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    73,
    82,
    98,
    122,
    172,
    174
   ],
   [
    20,
    27,
    74,
    83,
    96,
    120,
    173,
    175
   ],
   [
    21,
    31,
    75,
    84,
    100,
    124,
    174,
    179
   ],
   [
    22,
    32,
    76,
    85,
    101,
    125,
    175,
    177
   ],
   [
    23,
    30,
    77,
    86,
    99,
    123,
    176,
    178
   ],
   [
    24,
    34,
    78,
    87,
    92,
    103,
    127,
    177
   ],
   [
    25,
    35,
    79,
    88,
    90,
    104,
    128,
    178
   ],
   [
    26,
    33,
    80,
    89,
    91,
    102,
    126,
    179
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    2,
    9,
    18,
    29,
    36,
    37,
    38,
    47,
    54,
    63,
    74,
    81,
    82,
    83
   ]
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    96,
    105,
    115,
    123,
    124,
    125,
    133,
    141,
    150,
    160,
    168,
    169,
    170,
    178
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "origin": "submission",
  "construction": "Coset-based two-block (2BGA) code. Group G = metacyclic C30 |x C6 (action r=11, order 180); non-normal subgroup H=C2; qubits indexed by cosets G/H. H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with left/right coset actions; a,b element supports [0, 8, 34, 82] / [0, 54, 76, 162] found by simulated annealing. Weight-8 checks. A generalization of bivariate bicycle codes.",
  "model": "Claude Opus 4.8",
  "references": [
   "arXiv:2606.17268"
  ],
  "date": "2026-06-22",
  "notes": "Distance is an UPPER BOUND (d<=14): witnesses are explicit decoder-found logical operators of weight 14 (syndrome-decoder method), cross-checked by randomized minimum-weight search (QDistRnd-style); both saturate at 14 over 6e5 trials, and the sub-threshold logical-error slope corroborates d~14. NOT certified exact. This is a coset 2BGA on a non-abelian metacyclic group -- a generalization of bivariate bicycle, not standard BB on a torus. Three more variants with identical [[180,16,14]] parameters exist. These codes are NOT 2D-local (no planar layout) and enter only the weight-8 any-connectivity track -- unlike the planar weight-8 codes of arXiv:2504.08887, which also occupy the 2d-local tracks. The comparison is on (n,k,d) at check weight <= 8 only. PROVISIONAL: d=14 here is an UNVERIFIED upper bound (the witness only proves d<=14); exact certification is pending. A prior Gurobi ILP + LP-decoding-cut attempt on this code stalled with the per-generator lower bound at 8, but the source paper certified comparable n<=168 weight-8 coset codes by integer programming, so certification may yet succeed. Independent residual-weight and QDistRnd searches find NO logical below weight 14. If the true distance is below 14 the kd^2/n figure drops accordingly; treat any top-of-board ranking as provisional until certified."
 },
 "family": "2bga-coset"
}