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    64,
    82,
    105,
    153,
    167,
    172
   ],
   [
    2,
    18,
    65,
    83,
    106,
    154,
    165,
    173
   ],
   [
    3,
    22,
    66,
    84,
    110,
    158,
    169,
    174
   ],
   [
    4,
    23,
    67,
    85,
    108,
    156,
    170,
    175
   ],
   [
    5,
    21,
    68,
    86,
    109,
    157,
    168,
    176
   ],
   [
    6,
    25,
    69,
    87,
    113,
    161,
    172,
    177
   ],
   [
    7,
    26,
    70,
    88,
    111,
    159,
    173,
    178
   ],
   [
    8,
    24,
    71,
    89,
    112,
    160,
    171,
    179
   ]
  ]
 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    5,
    12,
    23,
    39,
    40,
    50,
    59,
    67,
    68,
    93,
    124,
    147,
    155,
    166
   ]
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    2,
    13,
    18,
    44,
    72,
    92,
    101,
    108,
    110,
    126,
    137,
    154,
    155,
    173
   ]
  }
 },
 "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, 50, 146, 172] / [0, 18, 55, 147] 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"
}