Coding theory aims at achieving efficient and reliable
trasmission of data over a noisy channel. Algebraically, an error
correcting code C is a subspace of a linear space and the data to be
transmitted is represented as vectors in C. Network coding is a recent
development in the theory of error correcting codes, which is
well-suited for transmitting data over a network. As the elements of a
linear code are points in a vector space, the elements of a network code
are points on a Grassmannian variety. In this talk, we introduce the
theory of error correcting codes, motivating the definition of network
coding. We then explain an algebraic construction of network codes,
which we obtained in collaboration with F. Manganiello and J. Rosenthal
(University of Zurich). Our construction has optimal distance properties
and an efficient decoding algorithm, which exploits the algebraic
structure of the code.


[Invited by Prof. Ruth Kellerhals and Dr. Laura Ciobanu]