Abstract
In recent years codes that are not Uniquely Decipherable (UD) were studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a free monoid showing the existence, in this poset, of maximal elements that we call full monoids. Then a set of generators of a full monoid is, by definition, a maximal set. We show how this definition extends, in a natural way, the existing definition concerning UD codes and we find a characteristic property of a monoid generated by a maximal UD code. Finally we generalize some properties of UD codes.
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