Cyclic Orbit Codes

TL;DR

This paper classifies cyclic orbit codes in network coding and proposes a decoding method for a specific subclass, enhancing understanding and decoding efficiency of these codes.

Contribution

It provides a comprehensive classification of cyclic orbit codes and introduces a decoding procedure for a particular subclass, advancing coding theory in network communications.

Findings

Classification of cyclic orbit codes completed

Decoding procedure for a subclass proposed

Potential improvements in network coding efficiency

Abstract

In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of F_q^n. If the acting group is cyclic, the corresponding orbit codes are called cyclic orbit codes. In this paper we give a classification of cyclic orbit codes and propose a decoding procedure for a particular subclass of cyclic orbit codes.