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 "provenance": {
  "authors": [
   "@pandey-tushar"
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  "origin": "submission",
  "novelty": "known_parameters",
  "construction": "Weight-5 coset two-block code (Aydin-Tamo-Barg construction) with a non-normal subgroup. G = D6 x Z28 (order 336), built as direct_product(dihedral(6)[0], cyclic_product(28)[0])[0] from research/kit/group_algebra.py, so element index = 28*i + j for D6 element i and Z28 element j. H = {0, 56, 182, 322} (order 4, not normal; |N_G(H)| = 112); qubits on the 84 left cosets G/H, n = 168. a = {0, 270, 211} acts on the left, b = {0, 18} acts on the right (b in N_G(H)); H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] via research/kit/coset.py build_coset. Found by a random sweep of weight-5 coset codes over non-normal subgroups of order 2-4.",
  "model": "Claude Opus 5",
  "references": [
   "arXiv:2606.17268",
   "arXiv:2306.16400"
  ],
  "date": "2026-09-18",
  "notes": "Known parameters: the Lin-Pryadko 2BGA catalogue (arXiv:2306.16400; github.com/QEC-pages/2BGA-codes @ 403d194) lists three weight-5 [[168,4,14]] codes as ordinary 2BGA codes over groups of order 84 (SmallGroup(84,3), (84,4), (84,13)). This entry is a coset code over a group of order 336 with a non-normal H, a different construction route; it has not been checked for equivalence to those catalogue codes (no GAP available). The verifier reports no exact duplicate and no WL-equivalent board entry."
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}