TL;DR
This paper explores longstanding open questions about the structure of finite maximal variable-length codes and their connections to factorizations of cyclic groups, aiming to advance understanding in coding theory.
Contribution
It discusses conjectures on finite maximal codes and links them to cyclic group factorizations, offering new perspectives on their structure.
Findings
Analysis of conjectures related to finite maximal codes
Connections established between code structures and cyclic group factorizations
Insights into longstanding open problems in coding theory
Abstract
Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Rings, Modules, and Algebras