Naj bo▫ $X$▫ podgrupa polne grupe avtomorfizmov Hammingovega grafa ▫$H(m,q)$▫, in ▫$C$▫ podmnožica vozlišč Hammingovega grafa. Rečemo, da je ▫$(X,2)$▫-sosednostno prehodna koda, če je ▫$X$▫ prehodna ...na ▫$C$▫, kot tudi na ▫$C_1$▫ in ▫$C_2$▫, množicah vozlišč, ki so na razdaljah 1 in 2 od kode. Pokazano je bilo, da če je dana ▫$(X,2)$▫-sosednostno-prehoden koda ▫$C$▫, potem obstaja podgrupa grupe ▫$X$▫ z 2-prehodnim delovanjem na abecedi; to delovanje je tako skoraj enostavno ali afino. Ta članek dopolnjuje klasifikacijo ▫$(X,2)$▫-sosednostno prehodnih kod, z minimalno razdaljo najmanj 5, kjer podgrupa grupe ▫$X$▫, ki stabilizira nekaj elementov, deluje skoraj enostavno na abecedi stabiliziranih elementov. Glavni rezultat tega članka pravi, da razred ▫$(X,2)$▫-sosednostno prehodnih kod s skoraj enostavnim delovanjem na abecedi in minimalno razdaljo najmanj 3 sestoji iz ene neskončne družine dobro znanih kod.
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