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nontrivial cyclotomic cosets of 2 all have size 16. The divisor g is a product of the minimal polynomials of 4 cyclotomic cosets of size 16, times x+1, of degree 65, which fixes k = 2 deg g = 130 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 14 and 14. 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 = 514 qubits at uniform row weight 28, with a = [24, 28, 37, 47, 49, 80, 88, 90, 91, 154, 174, 194, 223, 230] and b = [6, 7, 16, 48, 54, 71, 110, 115, 123, 133, 155, 224, 228, 240].", "notes": "Distance is an upper bound from the lighter of two witnesses, weight 46 on X and 52 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 46 to 57, with the minimum reached by exactly one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 54. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 46. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 122. The design point is deg g / m = 0.253." } }