Variable-Length Codes Independent or Closed with respect to Edit Relations

We investigate inference of variable-length codes in other domains of computer science, such as noisy information transmission or information retrieval-storage: in such topics, traditionally mostly constant-length codewords act. The study is relied upon the two concepts of independent and closed sets. We focus to those word relations whose images are computed by applying some peculiar combinations of deletion, insertion, or substitution. In particular, characterizations of variable-length codes that are maximal in the families of $\tau$-independent or $\tau$-closed codes are provided.