Variable-Length Codes Independent or Closed with respect to Edit Relations
Jean N\'eraud (LITIS, UNIROUEN)

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 -independent or -closed codes are provided.
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Taxonomy
TopicsDNA and Biological Computing · Algorithms and Data Compression · Cellular Automata and Applications
