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Gong (github.com/gongaa/RM127, triply-even/): Gong's doubly even self-dual [[65,1,13]] code doubled onto [[271,1,11]]; the doubling theorem (Jain and Albert, arXiv:2408.12752, Sec. III) gives d >= min(d_sd, d_tri + 2) = 13; 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":3.3452935677180777,"gamma_t":3.3452935677180777,"gamma_rho":3.3452935677180777,"gamma_claim":2.3368732056521524,"gamma_t_claim":2.3368732056521524,"gamma_rho_claim":2.3368732056521524,"v_ex":1,"rate":0.0024937655860349127,"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-401","N":104,"d":6,"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 [[65,1,13]] code doubled onto [[271,1,11]] (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"}]}