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"@vprusso" ], "construction": "Cyclic generalized bicycle at m=171 = 3 x 3 x 19, with ord_2(m)=18, so x^171 - 1 factors over GF(2) into 12 cyclotomic cosets, 1 of size 1, 1 of size 2, 1 of size 6, 9 of size 18. The divisor g is assembled from coset minimal polynomials to degree 20, which fixes k = 2 deg g = 40 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 7 and weight 9 in the two blocks. At least one weight is odd, so x+1 does not divide the gcd. m is composite, so the quotient fold acts at t=3, t=9, t=19 and t=57; a fold over every equal-orbit partition of the qubits returns nothing lighter than 48, clear of the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 342 qubits at uniform row weight 16, with a = [81, 87, 99, 107, 110, 133, 140] and b = [16, 49, 55, 91, 98, 143, 146, 151, 162].", "references": [], "date": "2026-10-15", "notes": "", "model": "Claude Opus 5" }, "family": "generalized-bicycle" }