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 },
 "distance": {
  "d": 20,
  "X": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
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   ]
  },
  "Z": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
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   ]
  }
 },
 "provenance": {
  "authors": [
   "Aydin, Arda",
   "Tamo, Itzhak",
   "Barg, Alexander"
  ],
  "construction": "Coset two-block group-algebra code (arXiv:2606.17268 Construction 1) on G = GAP SmallGroup(240,39) = C3 x ((C5 : C8) : C2) with non-normal subgroup H = C2 chosen as index s=1 in Filtered(AllSubgroups(G), K -> not IsNormal(G,K)) (GAP 4.14.0 ordering). Qubits are the m = [G:H] = 120 left cosets G/H; a = [1,37,136,228] indexes coset representatives in LeftCosets(G, Core(G,H)) (Core trivial, so 240 reps) acting on G/H by LEFT multiplication; b = [1,11,35,52] indexes coset representatives in LeftCosets(Normalizer(G,H), H) (|N_G(H)|=120, so 60 reps) acting on G/H by RIGHT multiplication. A = sum of the 4 left-action permutation matrices, B = sum of the 4 right-action matrices (Definition II.1 convention: M[i][j]=1 iff coset x_j H maps to x_i H); H_X = [A|B], H_Z = [B^T|A^T] over GF(2). Row 240 16 <=20 of Table VI (weight-8 section) of arXiv:2606.17268.",
  "references": [
   "arXiv:2606.17268"
  ],
  "date": "2026-07-14",
  "notes": "Literature baseline, seeded 2026-07-14. Published in arXiv:2606.17268 Table VI (weight-8 section) as [[240,16,<=20]]; the paper's d<=20 is a QDistRnd upper bound at 1e6 iterations, not exact. Recorded here as a witness-backed upper bound. Reproduction validated end to end in GAP 4.14.0 with the paper's exact Table II caption convention (s indexing Filtered(AllSubgroups(G), H -> not IsNormal(G,H)); a/b indexing LeftCosets(G, Core(G,H)) and LeftCosets(Normalizer(G,H), H) representatives; left/right coset actions per Definition II.1): the same pipeline reproduces Table VI rows [[80,8,10]] (SmallGroup(80,10), s=1), [[80,10,8]] (SmallGroup(80,10), s=1) and [[120,14,12]] (SmallGroup(120,32), s=3) with exact k and d matches. This reproduction's own screen (gf2_fast RIS, 8k/60k/200k/1M trials per ladder rung) also converges to d<=20 for this code. Seeding re-check by @willzeng agents 2026-07-14: 3 fresh seeds (950001-950003) x 2M trials/side (gf2_fast) all find lightest logical 20, nothing lighter.",
  "origin": "baseline"
 },
 "family": "2bga-coset"
}