FV code trees with no self-synchronizing string

It is shown in this paper that all internal nodes with the same subtree can be treated as a single state in a code tree of a fixed-to-variable length code (FV code) when we use CapocelliGrango-Vaccaro algorithm and Even algorithm to check whether the FV code has a self-synchronizing string. Based on this reduced state representation, we characterize three types of code trees with no self-synchronizing string and evaluate the number of code trees included in each type. The results of exhaustive search is also given for all code trees with 21 or less leaves.