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 "distance": {
  "d": 28,
  "X": {
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   "confidence": "upper_bound",
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    "found_by": [
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    "date": "2026-10-15",
    "found_at_samples": 400,
    "survived_samples": 400,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1
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    "date": "2026-10-15",
    "found_at_samples": 400,
    "survived_samples": 400,
    "tool": "research/kit/surrogate.lightest_logical",
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   }
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 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized bicycle at m=151, a prime with ord_2(m)=15, so the nontrivial cyclotomic cosets of 2 all have size 15 and the reachable divisor degrees are exactly 15j and 15j+1. The divisor g is the minimal polynomial of one coset of size 15 times x+1, of degree 16, which fixes k = 2 deg g = 32 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 6 in each block. Both weights are even, so x+1 divides the gcd; m is prime, so the only block logical this forces has weight m and is far above the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 302 qubits at uniform row weight 12, with a = [38, 43, 58, 99, 110, 145] and b = [33, 64, 79, 81, 106, 108].",
  "references": [],
  "date": "2026-10-15",
  "notes": "",
  "model": "Claude Opus 5"
 },
 "family": "generalized-bicycle"
}