Hall sets, Lazard sets and comma-free codes

TL;DR

This paper explores the connections between maximal comma-free codes and algebraic structures like Hall and Lazard sets, revealing new insights into their relationships and underlying algebraic properties.

Contribution

It establishes a link between comma-free codes and algebraic structures such as Hall and Lazard sets, providing a novel perspective on code construction.

Findings

Identifies relationships between comma-free codes and algebraic sets.

Provides new characterizations of maximal comma-free codes.

Bridges coding theory with algebraic structures.

Abstract

We investigate the relationship between two constructions of maximal comma-free codes described respectively by Eastman and by Scholtz and the notions of Hall sets and Lazard sets introduced in connection with factorizations of free monoids and bases of free Lie algebras.