It is known that the class of factorizing codes, i.e.,codes satisfying the factorization conjectureformulated by Schützenberger, isclosed under two operations:the classicalcomposition of codes and substitutionof codes.A natural question which arisesis whethera finite set Oof operations existssuch that each factorizingcode can be obtained by usingthe operations inO and starting with prefix or suffix codes.O is named herea complete setof operations (for factorizing codes).We show that composition and substitutionare not enough in order to obtaina completeset. Indeed, we exhibit a factorizing code over a two-letter alphabet A = {a,b}, precisely a 3-code, which cannot beobtained by decomposition or substitution.
