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

The class of completely transitive codes was introduced by Solé as a proper subclass of binary linear completely regular codes. There exist completely transitive codes with error-correcting capabilities = 1 2 and 3. In a previous correspondence, Borges and Rifà proved the nonexistence of completely transitive codes with more than two codewords and error-correcting capability 4. In this correspondence, we prove the nonexistence for the remaining case, namely, = 4. Therefore, the question of the existence of such codes, depending on their error-correcting capability, is completely solved.