Coding theory is a discipline at the crossroads between mathematics, computer science, and engineering. It concerns the transmission and storage of data over an imperfect channel, where the data may be altered or lost. Our daily life is made simpler and more comfortable by coding theory, which is used systematically in computers, hard drives, mobile phones, radios, digital scanners, and many other devices that we use everyday.

Deep space communication (as done by satellites) and transmission of data over the internet would be unthinkable without robust and efficient coding theoretic schemes. Other familiar examples of the use of coding theory in our daily lives are the AHV number, the ISBN book number, the PostKonto number, the IBAN, and the UPC barcodes, just to name a few. As mathematicians working in coding theory, our aim is providing the mathematical tools that make these applications possible, or that improve their efficiency.

This research plan focuses on the use of algebraic techniques in linear network coding. The aim of linear network coding is improving the efficiency and robustness of communication of several parties over a network. For example, network coding provides techniques for optimizing the transmission of data in digital file distribution (e.g., for internet distribution of software updates to a network of users), digital television, and peer-to-peer (P2P) file sharing.