It is known that the class
of factorizing codes, i.e.,
codes satisfying the factorization conjecture
formulated by Schützenberger, is
closed under two operations:
the classical
composition of codes and substitution
of codes.
A natural question which arises
is whether
a finite set O
of operations
exists
such that each factorizing
code can be obtained by using
the operations in
O and starting with prefix or suffix codes.
O is named here
a complete set
of operations (for factorizing codes).
We show that composition and substitution
are not enough in order to obtain
a complete
set. Indeed, we exhibit
a factorizing code over a two-letter alphabet A = {a,b}, precisely a 3-code, which cannot be
obtained by decomposition or substitution.