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 "distance": {
  "d": 21,
  "X": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
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  },
  "Z": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
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  }
 },
 "provenance": {
  "authors": [
   "@seunomonije"
  ],
  "construction": "Generalized bicycle (two-block) code on the cyclic group Z_127: H_X = [A|B], H_Z = [B^T|A^T] with A, B circulants; a(x) support {6,37,39,64,68,100,105,106} (weight 8), b(x) support {4,9,40,81,93,95,115,118} (weight 8), max check weight 16. Divisor trick: both a and b are sparse multiples of a degree-29 divisor g of x^127-1 (x^127-1 factors over GF(2) as (x+1) times eighteen degree-7 irreducibles; g here is (x+1) times four of the degree-7 factors, deg g = deg gcd(a,b,x^127-1) = 29, machine-verified), locking k = 2*29 = 58 before any linear algebra. Distance evidence: rising RIS ladder 20k/100k/400k/1.6M/2M trials (fresh seed per rung) flat at d<=21 at every rung; refutation barrage 8M trials x 3 fresh seeds (777/999/424242) at pair_depth 16 plus 3M trials x same seeds at pair_depth 24 (33M further trials) all bottoming at exactly d<=21; the 2M-trial witness search returned the embedded weight-21 X logical, and the GB transpose symmetry (block swap + index reversal i -> -i mod 127) maps it to the embedded weight-21 Z logical, both machine-verified against ker/rowspace.",
  "origin": "submission",
  "date": "2026-07-17",
  "model": "Claude Fable 5",
  "references": [
   "arXiv:1904.02703",
   "arXiv:2203.17216"
  ],
  "notes": "Search and verification by Claude Fable 5. First k=58 entry at n=254: beats [[254,44,24]] on kd^2/n (100.7 vs 99.8) and extends the n<=254 Pareto frontier in k (previous max k=44). Novelty vs the literature unverified. Deep-distance evidence: 16 sibling candidates from the same divisor sweep were laddered to 2M trials; this was the only one flat at 21 from 20k through 2M, and it survived a 33M-trial refutation barrage (3 seeds x 8M @ pair_depth 16, 3 seeds x 3M @ pair_depth 24) without moving."
 },
 "family": "generalized-bicycle"
}