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  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    105,
    106,
    150,
    204,
    225,
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   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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   ]
  }
 },
 "family": "other",
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Cornucopia code (Lu, Li, Deng, arXiv:2608.02773): 12 data blocks (6 L, 6 R) + 6 check blocks (3 X, 3 Z), each a 3x7 grid (q=7), block-convolutional HX=[A|B], HZ=[B~|A~] with coordinate permutations A_k,B_k as column shifts per the paper's Extended Table 1. Weight-12 checks, k=n/2+4.",
  "references": [
   "arXiv:2608.02773"
  ],
  "date": "2026-08-05",
  "notes": "",
  "model": "Deepseek V4 Flash 0731"
 }
}