New completely regular and completely transitive binary codes

Non-antipodal binary completely regular codes are considered. The only such codes come from binary perfect codes and specifically such new codes with covering radius ρ = 3 and ρ = 7 are constructed. In particular, a new binary completely regular code with minimal distance d = 8 and covering radius ρ = 7 has been built, which disproves the known conjecture of Neumaier from 1992, that the extended binary Golay [24, 12, 8]-code is the only binary completely regular code with d ≥ 8 and, also, an infinite family of binary completely regular codes with d = 4 and ρ = 3 is founded. It is proved that some of these new codes are also new completely transitive codes and, of course, new uniformly packed codes in the wide sense. As a corollary of the result on nonexistence of nontrivial binary perfect codes it is obtained that there are no unknown nontrivial non-antipodal completely regular binary codes with minimal distance d ≥ 3.