Abstract: Let L be a nonempty language over A, k∈N⁰ and m∈N. If L satisfies (LA^k)^mL∩A⁺(LA^k)^m-1LA⁺=Ø, then it is a code called (k,m)-comma code. If every singleton of L is a (k,m)-comma code, then it is called a 1-(k,m)-comma code. It is known that the class of 1-(k,m)-comma code is 2^Xk\{Ø}, where X_k ={u∈A⁺|(∠w∈A^k)uwu∩A⁺uA⁺=Ø}. Jürgensen et al. showed that X0 is the set of primitive words. Cui et al. gave a characterization of X1 in terms of bordered words, unbordered words, and primitive words. In this paper, we discuss X_k for any k≥2.

Key words: combinatorics of words, (k,m)-comma code, 1-(k,m)-comma code