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In two previous papers we constructed new families of completely regularcodes by concatenation methods. Here we determine cases in which the new codesare completely transitive. For these cases we also find the automorphism groupsof such codes. For the remaining cases, we show that the codes are notcompletely transitive assuming an upper bound on the order of the monomialautomorphism groups, according to computational results.

On new infinite families of completely regular and completely transitive codes