An enhanced property of factorizing codes

The investigation of the factorizing codes C, i.e., codes satisfying Schützenberger's factorization conjecture, has been carried out from different viewpoints, one of them being the description of structural properties of the words in C. In this framework, we can now improve an already published result. More precisely, given a factorizing code C over a two-letter alphabet A={a,b}, it was proved by De Felice that the words in the set C1=C∩a*ba* could be arranged over a matrix related to special factorizations of the cyclic groups. We now prove that, in addition, these matrices can be recursively constructed starting with those corresponding to prefix/suffix codes.