The finest homophonic partition and related code concepts

Let C be a finite set of n words having total length L where all words are taken over a R-element alphabet. The set C is called numerically decipherable if any two factorizations of the same word over the given alphabet into words in C have the same length. An O(nL² ) time and O((n+k)L) space algorithm is presented for computing the finest homophonic partition of C provided that this set is numerically decipherable. The latter property can be decided by another algorithm requiring O(nL) time and O((n+k)L) space. The two algorithms are based on a technique related to dominoes