Spread Codes and Spread Decoding in Network Coding

In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding algorithm of spread codes up to half the minimum distance

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

Construction of Codes for Network Coding

Based on ideas of K\"otter and Kschischang we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in Braun, Kerber and Laue as a purely combinatorial object. For the construction of network codes we successfully modified methods (construction with prescribed automorphisms) originally developed for the q-analogues of a combinatorial designs. We then give a special case of that method which allows the construction of network codes with a very large ambient space and we also show how to decode such codes with a very small number of operations

Recursive Code Construction for Random Networks

A modification of Koetter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same error-correcting capabilities. An efficient error-correcting algorithm is proposed for these codes.Comment: Submitted to IEEE Transactions on Information Theor

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

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.Comment: 5 pages; Submitted to IEEE International Symposium on Information Theory (ISIT) 201

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

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