Pl\"ucker Embedding of Cyclic Orbit Codes

TL;DR

This paper explores the Plücker embedding of cyclic orbit codes, enabling efficient computation of Grassmann coordinates, which enhances the understanding and application of these codes in network coding.

Contribution

It introduces methods for efficiently computing Grassmann coordinates of cyclic orbit codes via Plücker embedding, advancing their practical utility.

Findings

Efficient algorithms for Grassmann coordinate computation.

Enhanced understanding of cyclic orbit codes in the Plücker space.

Potential improvements in network coding performance.

Abstract

Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Pl\"ucker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words.