Abstract
In this paper, {\em e-word}s are used for coding Z_$k$_Z-ary trees with Z_$n$_Z internal nodes. The properties of e-words are discussed in depth, such as the necessary and sufficient condition of e-words, and based on the properties, a loopless algorithm is obtained to generate e-words for Z_$k$_Z-ary trees in lexicographic order, which is more efficient in both space and time than the previous algorithm. In addition, e-words can also be easily generated in lexicographic order by a recursive algorithm, and in the order with the Strong Minimal Change Property (SMCP) by a loopless algorithm.