{"id":"177.1.7.a","row":809,"stored":{"file":"master_catalog.json","row":809,"construction":null,"columns_sha256":null},"parameters":{"n":177,"k":1,"d":7,"N":47,"r":46,"level":3},"gate":{"string":"0","human":"T0","monomials":[[0]],"sk_key":[[0]],"sk_fingerprint":"bc179efd84e614ba","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2,3,4,6,7,9,10,12,13,14,15,16,17,18,19],[0,1,2,3,4,6,7,9,10,12,13,14,15,16,17,18,19],[0,2],[0,3],[0,4],[0,2,3,4,5,6,7,9,10,12,13,14,15,16,17,18,19],[0,6],[0,7],[0,2,3,4,6,7,8,9,10,12,13,14,15,16,17,18,19],[0,9],[0,10],[0,2,3,4,6,7,9,10,11,12,13,14,15,16,17,18,19],[0,12],[0,13],[0,14],[0,15],[0,16],[0,17],[0,18],[0,19],[0,2,3,4,6,7,9,10,12,13,14,15,16,17,18,19,20],[0,1,3,5,8,9,10,12,13,14,15,16,17,18,19],[0,1,2,5,7,12,13,14,15,16,17,18,19],[0,1,2,3,5,7,9,10,11,14,15,16,17,18,19],[0,1,3,4,5,6,7,8,12,13,14,16,17,18,19],[0,2,6,11,12,13,14,15,17,18,19],[0,1,5,6,8,9,10,11,12,13,15,16,19],[0,1,4,6,7,9,10,13,15,17,18,19,20],[0,4,8,9,10,11,15,17,18,19,20],[0,2,3,5,6,8,9,10,12,13,15,16,18,19,20],[0,4,8,9,10,12,14,15,16,17,18],[0,3,7,8,11,12,14,15,16,19,20],[0,1,2,4,5,6,8,9,11,13,15,16,17],[0,5,6,7,8,10,11,13,15,16,17],[0,1,2,6,8,10,14,16,17,19,20],[0,1,3,4,5,8,10,13,14,16,17,19,20],[0,1,3,4,5,8,10,11,14],[0,2,3,8,9,10,11,13,14],[0,2,3,4,5,7,11,13,14],[0,4,6,7,8,10,11,13,14],[0,1,2,7,8,12,15,16,17,19,20],[0,2,3,4,6,7,9,10,12,13,14,15,16,17,18,19,46],[0,1,2,3,4,6,7,9,10,12,13,14,15,16,17,18,19,46],[0,2,46],[0,3,46],[0,4,46],[0,2,3,4,5,6,7,9,10,12,13,14,15,16,17,18,19,46],[0,6,46],[0,7,46],[0,2,3,4,6,7,8,9,10,12,13,14,15,16,17,18,19,46],[0,9,46],[0,10,46],[0,2,3,4,6,7,9,10,11,12,13,14,15,16,17,18,19,46],[0,12,46],[0,13,46],[0,14,46],[0,15,46],[0,16,46],[0,17,46],[0,18,46],[0,19,46],[0,2,3,4,6,7,9,10,12,13,14,15,16,17,18,19,20,46],[0,1,3,5,8,9,10,12,13,14,15,16,17,18,19,46],[0,1,2,5,7,12,13,14,15,16,17,18,19,46],[0,1,2,3,5,7,9,10,11,14,15,16,17,18,19,46],[0,1,3,4,5,6,7,8,12,13,14,16,17,18,19,46],[0,2,6,11,12,13,14,15,17,18,19,46],[0,1,5,6,8,9,10,11,12,13,15,16,19,46],[0,1,4,6,7,9,10,13,15,17,18,19,20,46],[0,4,8,9,10,11,15,17,18,19,20,46],[0,2,3,5,6,8,9,10,12,13,15,16,18,19,20,46],[0,4,8,9,10,12,14,15,16,17,18,46],[0,3,7,8,11,12,14,15,16,19,20,46],[0,1,2,4,5,6,8,9,11,13,15,16,17,46],[0,5,6,7,8,10,11,13,15,16,17,46],[0,1,2,6,8,10,14,16,17,19,20,46],[0,1,3,4,5,8,10,13,14,16,17,19,20,46],[0,1,3,4,5,8,10,11,14,46],[0,2,3,8,9,10,11,13,14,46],[0,2,3,4,5,7,11,13,14,46],[0,4,6,7,8,10,11,13,14,46],[0,1,2,7,8,12,15,16,17,19,20,46],[0,21,22,26,27,28,30,46],[0,22,23,27,28,29,31,46],[0,21,22,23,24,26,27,29,46],[0,22,23,24,25,27,28,30,46],[0,23,24,25,26,28,29,31,46],[0,21,22,24,25,28,29,46],[0,22,23,25,26,29,30,46],[0,23,24,26,27,30,31,46],[0,21,22,24,25,26,30,31,46],[0,21,23,25,28,30,31,46],[0,21,24,27,28,29,30,31,46],[0,21,25,26,27,29,31,46],[0,21,46],[0,22,46],[0,23,46],[0,24,46],[0,25,46],[0,26,46],[0,27,46],[0,28,46],[0,29,46],[0,30,46],[0,31,46],[0,21,22,26,27,28,30,45,46],[0,22,23,27,28,29,31,45,46],[0,21,22,23,24,26,27,29,45,46],[0,22,23,24,25,27,28,30,45,46],[0,23,24,25,26,28,29,31,45,46],[0,21,22,24,25,28,29,45,46],[0,22,23,25,26,29,30,45,46],[0,23,24,26,27,30,31,45,46],[0,21,22,24,25,26,30,31,45,46],[0,21,23,25,28,30,31,45,46],[0,21,24,27,28,29,30,31,45,46],[0,21,25,26,27,29,31,45,46],[0,21,45,46],[0,22,45,46],[0,23,45,46],[0,24,45,46],[0,25,45,46],[0,26,45,46],[0,27,45,46],[0,28,45,46],[0,29,45,46],[0,30,45,46],[0,31,45,46],[0,33,39,45,46],[0,32,38,39,45,46],[0,32,38,45,46],[0,37,39,45,46],[0,33,34,36,45,46],[0,37,38,45,46],[0,35,39,45,46],[0,32,35,39,45,46],[0,32,35,45,46],[0,34,36,45,46],[0,34,45,46],[0,37,45,46],[0,37,38,39,45,46],[0,33,34,45,46],[0,35,45,46],[0,36,39,45,46],[0,33,36,39,45,46],[0,33,39,44,45,46],[0,32,38,39,44,45,46],[0,32,38,44,45,46],[0,37,39,44,45,46],[0,33,34,36,44,45,46],[0,37,38,44,45,46],[0,35,39,44,45,46],[0,32,35,39,44,45,46],[0,32,35,44,45,46],[0,34,36,44,45,46],[0,34,44,45,46],[0,37,44,45,46],[0,37,38,39,44,45,46],[0,33,34,44,45,46],[0,35,44,45,46],[0,36,39,44,45,46],[0,33,36,39,44,45,46],[0,40,41,44,45,46],[0,41,42,44,45,46],[0,40,41,42,44,45,46],[0,40,42,44,45,46],[0,40,44,45,46],[0,41,44,45,46],[0,42,44,45,46],[0,40,41,43,44,45,46],[0,41,42,43,44,45,46],[0,40,41,42,43,44,45,46],[0,40,42,43,44,45,46],[0,40,43,44,45,46],[0,41,43,44,45,46],[0,42,43,44,45,46],[0,43,44,45,46]]},"distance":{"d":7,"is_exact":false,"upper":9,"witness":[30,71,96,97,98,109,110,113,126],"A_d":null,"certified":{"d":9,"is_exact":false,"met":true,"source":"A. Gong (github.com/gongaa/RM127, triply-even/): Gong's doubly even self-dual [[41,1,9]] code doubled onto [[95,1,7]]; the doubling theorem (Jain and Albert, arXiv:2408.12752, Sec. III) gives d >= min(d_sd, d_tri + 2) = 9; the distances of Gong's self-dual [[41,1,9]] and [[65,1,13]] codes are proved here by enumerating every word of their stabiliser spaces"}},"clifford":{"kind":"none","correction":{"S":[],"CZ":[]},"rotation_powers":[]},"metrics":{"gamma":2.660014767427319,"gamma_t":2.660014767427319,"gamma_rho":2.660014767427319,"gamma_claim":2.3557672647413566,"gamma_t_claim":2.3557672647413566,"gamma_rho_claim":2.3557672647413566,"v_ex":1,"rate":0.005649717514124294,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Gong doubling: triply even family"],"discovery":"pre-existing","strongest_claim":"a code of the triply even family of A. Gong (note in github.com/gongaa/RM127, triply-even/; transversal_t_codes/): her doubly even self-dual [[41,1,9]] and [[65,1,13]] codes and quantum QR codes doubled onto [[95,1,7]], rebuilt here from her self-dual codes, where T on every qubit is a logical T or T-dagger; a verified witness, not a maximum","sources":[{"regime":"Gong doubling: triply even family","file":"transversal_t_codes/factories.json","label":"G-177","N":47,"d":7,"d_is_exact":false,"origin":"A. Gong, \"On some K=1 codes admitting strongly transversal T\", note in github.com/gongaa/RM127, triply-even/ (2025)","provenance":"Gong's doubly even self-dual [[41,1,9]] code doubled onto [[95,1,7]] (Gong's note)"}]},"references":[{"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"}]}