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    198
   ],
   [
    92,
    116,
    117,
    126,
    144,
    150,
    162,
    163,
    171
   ],
   [
    81,
    117,
    119,
    131,
    132,
    155,
    163,
    168,
    177
   ],
   [
    82,
    107,
    118,
    120,
    139,
    141,
    174,
    183,
    195
   ],
   [
    85,
    111,
    119,
    121,
    137,
    143,
    160,
    168,
    178
   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    80,
    82,
    83,
    88,
    100,
    101,
    107,
    110,
    136,
    148,
    152,
    158
   ]
  },
  "Z": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    2,
    26,
    34,
    36,
    80,
    85,
    97,
    102,
    107,
    108,
    114,
    118
   ]
  }
 },
 "provenance": {
  "authors": [
   "Bhardwaj, Aditya",
   "Ma, Muzhou",
   "Meister, Nadine",
   "King, Robbie",
   "Bluvstein, Dolev",
   "Preskill, John",
   "Cain, Madelyn",
   "Xu, Qian",
   "Huang, Hsin-Yuan"
  ],
  "construction": "Mitten code (arXiv:2607.28795, Definition 4): lifted product LP(A,B) over F2[G], G = GAP SmallGroup(40,5) = C4 x D10, base matrices A = [a0|a1], B = [b0|b1] from Table XIII, entries as 0-based indices into Elements(G): a0=[10, 21, 29], a1=[0, 17, 18], b0=[2, 27, 38], b1=[0, 19, 21]. Block form H_X = [[L(a0),0,L(a1),0,R(b0*)],[0,L(a0),0,L(a1),R(b1*)]], H_Z = [[R(b0),R(b1),0,0,L(a0*)],[0,0,R(b0),R(b1),L(a1*)]] with L(g)b(h)=b(gh), R(g)b(h)=b(h g^-1) and * the g->g^-1 involution (paper Definition 8). Check matrices taken from the authors' repository (github.com/a7b/yarn @ 82fb695a1e40, processor_codes/mitten). NOTE: for this code the Table XIII element indices correspond to a different (undocumented) ordering of Elements(G) than current GAP SmallGroup output, so the authors' published matrices are used verbatim; n, k, check weight 9 and the canonical logical operator weights of Table I were all verified against the paper.",
  "references": [
   "arXiv:2607.28795"
  ],
  "date": "2026",
  "notes": "Literature baseline. Paper claims d = 12 (exact, via sQetch + BP+OSD estimators; not certified here). Seeded per issue #377.",
  "origin": "baseline"
 },
 "family": "lifted-product"
}