A complete characterization of irreducible cyclic orbit codes and their Plücker embedding

Authors:
Joachim Rosenthal;Anna-Lena Trautmann
Affiliations:
Institute of Mathematics, University of Zurich, Zurich, Switzerland;Institute of Mathematics, University of Zurich, Zurich, Switzerland
Venue:
Designs, Codes and Cryptography
Year:
2013

Citing 5
Cited 0

Introduction to finite fields and their applications

Introduction to finite fields and their applications
Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

Mathematical Methods in Computer Science
Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams

IEEE Transactions on Information Theory
Network information flow

IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as orbits of a subgroup of the general linear group on the Grassmannian. This paper gives a complete characterization of orbit codes that are generated by an irreducible cyclic group, i.e. a group having one generator that has no non-trivial invariant subspace. We show how some of the basic properties of these codes, the cardinality and the minimum distance, can be derived using the isomorphism of the vector space and the extension field. Furthermore, we investigate the Plücker embedding of these codes and show how the orbit structure is preserved in the embedding.