Code loops: automorphisms and representations

TL;DR

This paper constructs free Moufang loops within the variety generated by code loops and thoroughly studies their structure, including defining and classifying all basic representations for code loops of ranks 3 and 4.

Contribution

It introduces a construction of free Moufang loops in the code loop variety and classifies all basic representations for low-rank code loops.

Findings

Constructed free Moufang loops in the code loop variety.

Determined all basic representations of code loops of rank 3 and 4.

Abstract

In this work we construct free Moufang loop in the variety generated by code loops. We apply this construction for study the code loops. Moreover, we define and determine all basic representations of code loops of rank 3 and 4.