On a complete set of operations for factorizing codes
It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schutzenberger, 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.
variable length codes formal languages factorizations of cyclic groups