The finest homophonic partition and related code concepts

Abstract

Let C be a finite set of n words having total length L where all words are taken over a k-element alphabet. The set C is 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. Whether or not the set C is numerically decipherable can be decided by another algorithm requiring O(nL) time and O((n + k)L) space. These algorithms are based on a recently developed technique related to dominoes. The presentation includes similar procedures which decide in O(nL) time and O((n+k)L) space whether or not C is uniquely decipherable and in O(n2L) time and O((n + k)L) space whether or not C is multiset decipherable.