{
 "schema_version": "0.3",
 "name": "[[28,4,6]]",
 "code_type": "CSS",
 "n": 28,
 "k": 4,
 "checks": {
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 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    7,
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    26
   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    9,
    10,
    14,
    15
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA (two-block group algebra) code on group ab(7,2) (|G|=14); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 3, 7, 12], b = [0, 4, 9, 13] as element indices of the Cayley table (identity = 0; table convention in the note)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Opus 5.5",
  "search_budget": {
   "candidates_screened": 23560000,
   "ris_trials_per_side": 30000000,
   "cpu_hours": 3,
   "tool": "research/kit 2BGA sweep + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
     5792,
     5803,
     5839,
     5845
    ]
   },
   "X": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
     8045,
     8061,
     8368,
     8415
    ]
   }
  },
  "rounds": 6,
  "stim_version": "1.16.0",
  "notes": "Interleaved two-block extraction (Bravyi et al. arXiv:2308.07915 Table 5 style): joint reset and measurement layers, 9 CX layers per round; X-check term slots [2, 7, 6, 1, 3, 5, 8, 4], Z-check term slots [6, 1, 2, 7, 4, 3, 0, 5] over terms A_0..A_3, B_0..B_3; terms recovered from H alone by a commuting permutation decomposition; generated by qldpc submit (research/circuit_autogen.py, seed 0), the first of up to 6 candidates whose RIS screen at 2 rounds found nothing below d; witnesses from RIS on ker(H_dem) at twice the gate's trial budget, validated in GF(2)"
 }
}