On the factor set of code loops

TL;DR

This paper investigates the algebraic properties of code loops derived from doubly even binary linear codes with factor sets, establishing their classification as central, conjugacy closed, Burn, and extra loops, and deriving identities for their factor sets.

Contribution

It characterizes the algebraic structure of code loops with factor sets, showing they possess multiple loop properties and providing general identities for their factor sets.

Findings

Code loops are central, conjugacy closed, Burn, and extra loops.

Derived general identities for the factor sets of code loops.

Abstract

A Code loop on a binary linear code that is doubly even with a factor set is shown to be a central loop, conjugacy closed loop, Burn loop and extra loop. General forms of the identities that define the factor set of a code are deduced.