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"Cyclic generalized-bicycle code on the ring x^257 - 1 with a(x) = x^8 + x^43 + x^82 + x^89 + x^95 + x^100 + x^143 + x^165 + x^208 + x^213 + x^219 + x^226, b(x) = x^9 + x^21 + x^57 + x^77 + x^97 + x^103 + x^132 + x^155 + x^184 + x^190 + x^210 + x^230; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]. a and b are low-weight codewords of the ideal of a divisor of x^257 - 1 of degree 65, fixing k = 2 deg gcd(a, b, x^m - 1) = 130.", "notes": "Designed-divisor construction: the divisor is a product of cyclotomic-coset minimal polynomials over GF(2^ord_2(m)), so its degree and hence k are chosen rather than inherited, and a and b are drawn from its ideal by information-set decoding. Distance is a witness-backed upper bound: both witnesses are orbit-fold logicals (the fold the PR gate runs, verify/heuristic_distance.py), constant on the orbits of the code's block reflections and lighter than anything 24 random information-set seeds at 2,000,000 trials each or 300,000,000 GPU trials per side found; both re-verified against these matrices." } }