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and Albert (arXiv:2408.12752), Table I: [[101,1,17]] code of the self-dual [102,51,18] code sub(XQ103) doubled onto [[575,1,15]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 17, with d_sd at least the classical distance less one (their Lemma 2.4); the [[69,1,13]] input's distance is proved here by enumerating every word of SD70 through the punctured coordinate"}},"clifford":{"kind":"powers","correction":{"S":[[1,2],[2,2],[3,2],[4,2],[8,2],[10,2],[12,2],[16,2],[17,2],[21,2],[26,2],[27,2],[28,2],[33,2],[35,2],[36,2],[37,2],[38,2],[42,2],[45,2],[48,2],[50,2],[101,2],[102,2],[103,2],[104,2],[105,2],[106,2],[107,2],[108,2],[109,2],[110,2],[111,2],[112,2],[113,2],[114,2],[115,2],[116,2],[117,2],[118,2],[119,2],[120,2],[121,2],[122,2],[123,2],[147,2],[150,2],[151,2],[154,2],[155,2],[157,2],[158,2],[161,2],[164,2],[166,2],[194,2],[196,2],[198,2]],"CZ":[[1,198],[2,198],[3,198],[4,198],[8,198],[10,198],[12,198],[16,198],[17,198],[21,198],[26,198],[27,198],[28,198],[33,198],[35,198],[36,198],[37,198],[38,198],[42,198],[45,198],[48,198],[50,198],[101,196],[102,196],[103,196],[104,196],[105,196],[106,196],[107,196],[108,196],[109,196],[110,196],[111,196],[112,196],[113,196],[114,196],[115,196],[116,196],[117,196],[118,196],[119,196],[120,196],[121,196],[122,196],[123,196],[147,194],[150,194],[151,194],[154,194],[155,194],[157,194],[158,194],[161,194],[164,194],[166,194]]},"rotation_powers":[[0,3],[3,3],[6,3],[7,3],[8,3],[9,3],[10,3],[11,3],[14,3],[16,3],[19,3],[20,3],[24,3],[27,3],[31,3],[32,3],[33,3],[37,3],[40,3],[41,3],[43,3],[44,3],[46,3],[47,3],[48,3],[51,3],[101,3],[104,3],[107,3],[108,3],[109,3],[110,3],[111,3],[112,3],[115,3],[117,3],[120,3],[121,3],[125,3],[128,3],[132,3],[133,3],[134,3],[138,3],[141,3],[142,3],[144,3],[145,3],[147,3],[148,3],[149,3],[152,3],[362,3],[363,3],[364,3],[365,3],[366,3],[367,3],[371,3],[373,3],[374,3],[377,3],[378,3],[383,3],[385,3],[387,3],[388,3],[389,3],[393,3],[394,3],[431,3],[432,3],[433,3],[434,3],[435,3],[436,3],[440,3],[442,3],[443,3],[446,3],[447,3],[452,3],[454,3],[456,3],[457,3],[458,3],[462,3],[463,3],[593,3],[596,3],[597,3],[603,3],[604,3],[605,3],[606,3],[607,3],[608,3],[610,3],[611,3],[612,3],[615,3],[636,3],[637,3],[639,3],[640,3],[643,3],[644,3],[645,3],[646,3],[647,3],[654,3],[658,3],[659,3],[661,3],[662,3],[663,3],[664,3],[665,3],[666,3],[667,3],[668,3],[669,3],[670,3],[671,3],[672,3],[673,3],[674,3],[675,3],[676,3],[677,3],[678,3],[679,3],[680,3],[682,3],[686,3],[687,3],[688,3],[690,3],[692,3],[704,3],[705,3],[709,3],[710,3],[711,3],[713,3],[715,3],[727,3],[729,3],[730,3],[732,3],[738,3],[744,3],[745,3],[748,3],[750,3],[751,3],[752,3],[753,3],[754,3],[756,3],[757,3],[758,3],[759,3],[760,3]]},"metrics":{"gamma":3.7144719839181404,"gamma_t":3.7144719839181404,"gamma_rho":3.7144719839181404,"gamma_claim":2.349078428678893,"gamma_t_claim":2.349078428678893,"gamma_rho_claim":2.349078428678893,"v_ex":1,"rate":0.001287001287001287,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling: triorthogonal family"],"discovery":"pre-existing","strongest_claim":"a code of the triorthogonal family of Jain and Albert (arXiv:2408.12752, Table I; transversal_t_codes/), self-dual CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction; a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling: triorthogonal family","file":"transversal_t_codes/factories.json","label":"JA-777","N":199,"d":6,"d_is_exact":false,"origin":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance\", IEEE J. Sel. Areas Inf. Theory 6, 127 (2025), arXiv:2408.12752","provenance":"[[101,1,17]] code of the self-dual [102,51,18] code sub(XQ103) doubled onto [[575,1,15]] (Table I)","notes":"its [[69,1,13]] input is the self-dual [70,35,12] code found by transversal_t_codes/search_sd70.py, whose words through the punctured coordinate all weigh at least 14, in place of the paper's [70,35,14] code, which is only formally self-dual"}]},"references":[{"key":"jain2025transversal","short":"Jain & Albert (2025)","full":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance,\" IEEE J. Sel. Areas Inf. Theory 6, 127-137 (2025); arXiv:2408.12752.","url":"https://doi.org/10.1109/JSAIT.2025.3570832","date":"2025-05-16"}]}