Nonexistence of completely transitive codes with error-correcting capability e>3

The class of completely transitive codes was introduced by Sole (1990) as a proper subclass of binary linear completely regular codes. There exist completely transitive codes with error-correcting capabilities e=1, 2, and 3. In a previous correspondence, Borges and Rifa (see ibid., vol.46, no.1, p.279-80, Jan. 2000) proved the nonexistence of completely transitive codes with more than two codewords and error-correcting capability e>4. In this correspondence, we prove the nonexistence for the remaining case, namely, e=4. Therefore, the question of the existence of such codes, depending on their error-correcting capability, is completely solved