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351, 352, 354, 356, 371, 378, 381, 382, 392, 401, 403, 408, 417, 426, 428, 434 ], [ 328, 330, 331, 352, 353, 355, 357, 372, 379, 382, 383, 393, 402, 404, 409, 418, 427, 429, 435 ], [ 329, 331, 332, 353, 354, 356, 358, 373, 380, 383, 384, 394, 403, 405, 410, 419, 428, 430, 436 ], [ 330, 332, 333, 354, 355, 357, 359, 374, 381, 384, 385, 395, 404, 406, 411, 420, 429, 431, 437 ], [ 331, 333, 334, 355, 356, 358, 360, 375, 382, 385, 386, 396, 405, 407, 412, 421, 430, 432, 438 ], [ 332, 334, 335, 356, 357, 359, 361, 376, 383, 386, 387, 397, 406, 408, 413, 422, 431, 433, 439 ], [ 333, 335, 336, 357, 358, 360, 362, 377, 384, 387, 388, 398, 407, 409, 414, 423, 432, 434, 440 ], [ 334, 336, 337, 358, 359, 361, 363, 378, 385, 388, 389, 399, 408, 410, 415, 424, 433, 435, 441 ] ] }, "distance": { "d": 7, "X": { "value": 7, "confidence": "upper_bound", "witness": [ 104, 106, 108, 109, 130, 131, 133 ] }, "Z": { "value": 7, "confidence": "upper_bound", "witness": [ 26, 47, 49, 51, 130, 154, 155 ] } }, "provenance": { "authors": [ "@hirobumii" ], "construction": "G=C26, addition modulo26. A and B are1x4 rows with respective entry supports[[0, 1, 2], [0, 1, 3, 5], [0, 3, 5, 12], [0, 6, 8, 17]] and[[0, 1, 3], [0, 2, 4, 5], [0, 1, 4, 11], [0, 5, 7, 16]]. Each entry is the binary sum of its cyclic permutation matrices. Sixteen VV(k,j) blocks indexed4*k+j precede one CC block, allsize26. X(j,r) places A(k) on VV(k,j), with column r+g, and B(j) on CC. Z(k,r) places B(j)^T on VV(k,j), with column r-g, and A(k)^T on CC. All104 original rows per sector are independent and retained.", "references": [ "https://arxiv.org/abs/2111.03654", "https://arxiv.org/abs/2607.28795" ], "date": "2026-10-18", "notes": "Displayed presentation: maximum check weight 19, maximum qubit degree 30, 208 checks and total incidence 3900.", "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)" }, "family": "lifted-product" }