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

TL;DR

This paper explores the properties of variable-length codes that are either independent or closed under certain edit operations, providing characterizations of maximal codes in these families.

Contribution

It introduces new characterizations of maximal variable-length codes that are independent or closed under specific edit relations, extending understanding beyond constant-length codes.

Findings

Characterizations of maximal $ au$-independent codes

Characterizations of maximal $ au$-closed codes

Extension of code theory to variable-length codes under edit relations

Abstract

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.