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

A Complete Characterization of Irreducible Cyclic Orbit Codes and their Pl\"ucker Embedding

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 Pl\"ucker embedding of these codes and show how the orbit structure is preserved in the embedding.Comment: submitted to Designs, Codes and Cryptograph

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

Survey of Inter-satellite Communication for Small Satellite Systems: Physical Layer to Network Layer View

Small satellite systems enable whole new class of missions for navigation, communications, remote sensing and scientific research for both civilian and military purposes. As individual spacecraft are limited by the size, mass and power constraints, mass-produced small satellites in large constellations or clusters could be useful in many science missions such as gravity mapping, tracking of forest fires, finding water resources, etc. Constellation of satellites provide improved spatial and temporal resolution of the target. Small satellite constellations contribute innovative applications by replacing a single asset with several very capable spacecraft which opens the door to new applications. With increasing levels of autonomy, there will be a need for remote communication networks to enable communication between spacecraft. These space based networks will need to configure and maintain dynamic routes, manage intermediate nodes, and reconfigure themselves to achieve mission objectives. Hence, inter-satellite communication is a key aspect when satellites fly in formation. In this paper, we present the various researches being conducted in the small satellite community for implementing inter-satellite communications based on the Open System Interconnection (OSI) model. This paper also reviews the various design parameters applicable to the first three layers of the OSI model, i.e., physical, data link and network layer. Based on the survey, we also present a comprehensive list of design parameters useful for achieving inter-satellite communications for multiple small satellite missions. Specific topics include proposed solutions for some of the challenges faced by small satellite systems, enabling operations using a network of small satellites, and some examples of small satellite missions involving formation flying aspects.Comment: 51 pages, 21 Figures, 11 Tables, accepted in IEEE Communications Surveys and Tutorial