The second step in characterizing a three-word code

In the fields of combinatorics on words and theory of codes, a two-word language {x, y} is a code if and only if xy ≠ yx . But up to now, corresponding characterizations for a three-word language, which forms a code, have not been completely found. Let X={x, y, z} be a three-word language and |x|, |y|, |z| be their lengths. When |x| = |y| < |z| , a necessary and sufficient condition for X to be a code was obtained in 2018. If |x| < |y| = |z| ≤ 2|x| , a necessary and sufficient condition for X to be a code is proposed in this paper.