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here by the doubling of Jain and Albert (arXiv:2408.12752) from A. Gong's [[559,1,15]] (github.com/gongaa/RM127, triply-even/): [[103,1,19]] quantum QR code (extended QR [104,52,20]) doubled onto [[761,1,17]]; their doubling theorem (Sec. III) gives d >= min(d_sd, d_tri + 2) = 19, with d_sd at least the classical distance less one (their Lemma 2.4) and the distances of Gong's self-dual [[41,1,9]] and [[65,1,13]] codes proved here by enumerating every word of their stabiliser spaces"}},"clifford":{"kind":"powers","correction":{"S":[[0,1],[52,2],[53,2],[54,2],[55,2],[59,2],[61,2],[63,2],[67,2],[68,2],[72,2],[77,2],[78,2],[79,2],[84,2],[86,2],[87,2],[88,2],[89,2],[93,2],[96,2],[99,2],[101,2],[245,2]],"CZ":[[52,245],[53,245],[54,245],[55,245],[59,245],[61,245],[63,245],[67,245],[68,245],[72,245],[77,245],[78,245],[79,245],[84,245],[86,245],[87,245],[88,245],[89,245],[93,245],[96,245],[99,245],[101,245]]},"rotation_powers":[[0,7],[1,7],[3,7],[8,7],[9,7],[12,7],[13,7],[14,7],[15,7],[17,7],[18,7],[19,7],[20,7],[26,7],[28,7],[29,7],[30,7],[31,7],[32,7],[35,7],[37,7],[42,7],[43,7],[44,7],[48,7],[49,7],[51,7],[105,3],[107,3],[108,3],[109,3],[110,3],[113,3],[114,3],[119,3],[124,3],[125,3],[126,3],[127,3],[128,3],[130,3],[136,3],[137,3],[139,3],[141,3],[142,3],[143,3],[144,3],[148,3],[149,3],[150,3],[153,3],[155,3],[156,3],[157,3],[158,3],[159,3],[160,3],[161,3],[162,3],[163,3],[164,3],[165,3],[166,3],[167,3],[168,3],[169,3],[170,3],[171,3],[172,3],[173,3],[174,3],[175,3],[176,3],[177,3],[178,3],[179,3],[180,3],[181,3],[182,3],[183,3],[184,3],[185,3],[186,3],[187,3],[188,3],[189,3],[190,3],[191,3],[192,3],[193,3],[194,3],[195,3],[196,3],[197,3],[198,3],[199,3],[200,3],[201,3],[202,3],[203,3],[204,3],[205,3],[206,3],[209,3],[212,3],[213,3],[214,3],[215,3],[216,3],[217,3],[220,3],[222,3],[225,3],[226,3],[230,3],[233,3],[237,3],[238,3],[239,3],[243,3],[246,3],[247,3],[249,3],[250,3],[252,3],[253,3],[254,3],[257,3],[307,3],[310,3],[313,3],[314,3],[315,3],[316,3],[317,3],[318,3],[321,3],[323,3],[326,3],[327,3],[331,3],[334,3],[338,3],[339,3],[340,3],[344,3],[347,3],[348,3],[350,3],[351,3],[353,3],[354,3],[355,3],[358,3]]},"metrics":{"gamma":3.8365632293350793,"gamma_t":3.8365632293350793,"gamma_rho":3.8365632293350793,"gamma_claim":2.334637784682281,"gamma_t_claim":2.334637784682281,"gamma_rho_claim":2.334637784682281,"v_ex":1,"rate":0.001034126163391934,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling of Gong's codes"],"discovery":"pre-existing","strongest_claim":"a code built here by the doubling method of Jain and Albert (arXiv:2408.12752) from the codes in A. Gong's repository (github.com/gongaa/RM127, triply-even/): her [[559,1,15]] doubled with the self-dual CSS codes of the paper's Table I from distance 17 on (transversal_t_codes/); a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling of Gong's codes","file":"transversal_t_codes/factories.json","label":"GJ-967","N":247,"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; A. Gong, \"On some K=1 codes admitting strongly transversal T\", note in github.com/gongaa/RM127, triply-even/ (2025)","provenance":"[[103,1,19]] quantum QR code (extended QR [104,52,20]) doubled onto [[761,1,17]]: the doubling method of Jain and Albert (arXiv:2408.12752) applied to the codes in A. Gong's repository (github.com/gongaa/RM127)"}]},"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"},{"key":"gong2025triply","short":"Gong (2025)","full":"A. Gong, \"On some K=1 codes admitting strongly transversal T,\" note in the RM127 repository, triply-even/ (2025).","url":"https://github.com/gongaa/RM127/tree/main/triply-even","date":"2025-04-10"}]}