On non-antipodal binary completely regular codes

Binary non-antipodal completely regular codes are characterized. Using the result on nonexistence of nontrivial binary perfect codes, it is concluded that there are no unknown nontrivial non-antipodal completely regular binary codes with minimum distance d ≥ 3. The only such codes are halves and punctered halves of known binary perfect codes. Thus, new such codes with covering radiuses ρ = 2, 3, 6 and ρ = 7 are obtained. In particular, a half of the binary Golay [23, 12, 7]-code is a new binary completely regular code with minimum distance d = 8 and covering radius ρ = 7. The punctured half of the Golay code is a new completely regular code with minimum distance d = 7 and covering radius ρ = 6. That new code with d = 8 disproves the known conjecture of Neumaier, that the extended binary Golay [24, 12, 8]-code is the only binary completely regular code with d ≥ 8. Halves of binary perfect codes with Hamming parameters also provide an infinite family of new binary completely regular codes with d = 4 and ρ = 3. Puncturing of these codes also provide an infinite family of binary completely regular codes with d = 3 Preprint submitted to Elsevier Science 13 June 2005 and ρ = 2. Some of these new codes are also new completely transitive codes. Of course, all these new codes are new uniformly packed codes in the wide sense.