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314, 378 ], [ 209, 223, 228, 301, 309, 315, 379 ], [ 184, 224, 231, 258, 302, 316, 380 ], [ 211, 225, 230, 303, 311, 317, 381 ], [ 186, 226, 233, 260, 304, 318, 382 ], [ 213, 227, 232, 235, 305, 319, 383 ], [ 157, 188, 228, 262, 306, 320, 384 ], [ 156, 215, 229, 237, 307, 321, 385 ], [ 159, 190, 230, 264, 308, 322, 386 ], [ 158, 217, 231, 239, 309, 323, 387 ], [ 161, 192, 232, 266, 310, 324, 388 ], [ 160, 219, 233, 241, 311, 325, 389 ] ] }, "distance": { "d": 10, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 4, 40, 48, 74, 82, 114, 121, 122, 152, 155 ] }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 91, 105, 131, 145, 234, 243, 247, 274, 281, 287 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Lifted product over the non-abelian group algebra F_2[G], G = Z_39 x|_14 Z_2 (order 78; generators x, y with x^39 = y^2 = 1, y x = x^14 y; element x^a y^b has index a*2+b). Base matrices A = [1 + x^17 + x^33y^1, 1 + x^7] (entries act by the left regular representation L(g)[gh,h]=1) and B = [1 + x^20 + x^36y^1, 1 + x^22] (entries act by the right regular representation R(g)[h,hg]=1). Element index lists: A = [[[0, 34, 67], [0, 14]]], B = [[[0, 40, 73], [0, 44]]]. Qubit blocks of size |G|: sector 1 holds (i,j) for i in cols(A), j in cols(B) at block i*n_B+j; sector 2 holds (r,s) for r in rows(A), s in rows(B). X-check (r,j) = [L(A[r][i]) on (i,j)] + [R(B[s][j]) on (r,s)]; Z-check (i,s) = [R(B[s][j])^T on (i,j)] + [L(A[r][i])^T on (r,s)]. Same construction as the weight-9 mitten / ZSZ-LP codes of arXiv:2607.28795 and arXiv:2607.27644 (four weight-3 entries there), here with entry weights (3,2)/(3,2), check weight 8. Built with research/kit/nonabelian_lp.lifted_product_base.", "origin": "submission", "date": "2026-09-20", "model": "Claude Fable 5.1", "notes": "Distance is a witness-backed upper bound from randomized information-set search (research/kit/surrogate.distance_rand, gf2_fast backend); screen 400 trials, ladder [10, 10, 10], packaging 300000 trials per side. Advances the unrestricted weight-8 board cell; novelty vs the literature unverified.", "search_budget": { "candidates_screened": 26210, "ris_trials_per_side": 300000, "wall_clock_hours": 1.0, "tool": "research/kit search funnel, gf2_fast RIS" } }, "family": "lifted-product" }