On conjugacy classes of subgroups of the general linear group and cyclic orbit codes

TL;DR

This paper classifies conjugacy classes of cyclic subgroups in the general linear group to better understand and classify cyclic orbit codes used in network communication, simplifying their study.

Contribution

It provides a classification of conjugacy classes of cyclic subgroups of the general linear group, narrowing the focus for studying cyclic orbit codes.

Findings

Classification of conjugacy classes of cyclic subgroups

Reduced the study of cyclic orbit codes to a specific subgroup family

Facilitated analysis of orbit codes in network communication

Abstract

Orbit codes are a family of codes employable for communications on a random linear network coding channel. The paper focuses on the classification of these codes. We start by classifying the conjugacy classes of cyclic subgroups of the general linear group. As a result, we are able to focus the study of cyclic orbit codes to a restricted family of them.