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205, 221, 297, 299, 349, 377 ], [ 169, 222, 232, 272, 300, 350, 378 ], [ 168, 207, 223, 299, 301, 351, 379 ], [ 156, 171, 224, 274, 302, 352, 380 ], [ 170, 209, 225, 301, 303, 353, 381 ], [ 158, 173, 226, 276, 304, 354, 382 ], [ 172, 211, 227, 303, 305, 355, 383 ], [ 160, 175, 228, 278, 306, 356, 384 ], [ 174, 213, 229, 305, 307, 357, 385 ], [ 162, 177, 230, 280, 308, 358, 386 ], [ 176, 215, 231, 307, 309, 359, 387 ], [ 164, 179, 232, 282, 310, 360, 388 ], [ 178, 217, 233, 309, 311, 361, 389 ] ] }, "distance": { "d": 9, "X": { "value": 9, "confidence": "upper_bound", "witness": [ 52, 86, 92, 107, 114, 136, 142, 286, 364 ] }, "Z": { "value": 9, "confidence": "upper_bound", "witness": [ 14, 39, 63, 167, 195, 198, 217, 266, 344 ] } }, "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "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^11y^1 + x^36, 1 + x^25] (entries act by the left regular representation L(g)[gh,h]=1) and B = [1 + x^27y^1 + x^34, 1 + x^14] (entries act by the right regular representation R(g)[h,hg]=1). 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 (which are the case of four weight-3 entries), here with entry weights [[3, 2]] / [[3, 2]].", "references": [ "arXiv:2607.28795", "arXiv:2607.27644", "arXiv:2111.03654" ], "date": "2026-09-16", "notes": "Distance is a witnessed upper bound (both sides weight 9). Depth: screen at 300 fast RIS trials read d <= 9, ladder 10k and 100k trials read 9, 9; at packaging two independent fast RIS (gf2_fast) two-sided searches of 1,000,000 trials per side (seeds 7919 and 15838) each returned a weight-9 X logical and nothing lighter on either side. Gate refutation seed 559191786. Novelty: no [[390,78,9]] and no isomorphic code found in the 2BGA, GB, BB, QECDB and codetables data (Tanner-graph canonical-form check with pynauty); parameters claimed new, not verifier-proved. Not equivalent to a board entry (validator dedup found no exact or WL-equivalent match). Sampler spec: {\"family\": \"nonabelian-lp\", \"group\": \"ZSZ(39,2,14)\", \"N\": 78, \"A\": [[[0, 23, 72], [0, 50]]], \"B\": [[[0, 55, 68], [0, 28]]], \"w\": 8}" }, "family": "lifted-product" }