Message Encoding for Spread and Orbit Codes

Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability and transmission rate, but the question of how to encode messages has not been investigated. In this work we show how the message space can be chosen for a given code and how message en- and decoding can be done.Comment: Submitted to IEEE International Symposium on Information Theory 201

Isometry and Automorphisms of Constant Dimension Codes

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived

Pl\"ucker Embedding of Cyclic Orbit Codes

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.Comment: to appear in Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems 2012, Melbourne, Australi

New Lower Bounds for Constant Dimension Codes

This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension codes are presented. The examples of codes obtained by these constructions are the largest known constant dimension codes for the given parameters

A Complete Characterization of Irreducible Cyclic Orbit Codes

We give a complete list of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We derive some of the basic properties of these codes such as the cardinality and the minimum distance.Comment: in Proceedings of The Seventh International Workshop on Coding and Cryptography 2011 April 11-15 2011, Paris, Franc