We consider the problem of information flow over Gaussian relay networks.
Similar to the recent work by Avestimehr \emph{et al.} [1], we propose network
codes that achieve up to a constant gap from the capacity of such networks.
However, our proposed codes are also computationally tractable. Our main
technique is to use the codes of Avestimehr \emph{et al.} as inner codes in a
concatenated coding scheme.

We consider the problem of optimally allocating a given total storage budget
in a distributed storage system. A source has a data object which it can code
and store over a set of storage nodes; it is allowed to store any amount of
coded data in each node, as long as the total amount of storage used does not
exceed the given budget. A data collector subsequently attempts to recover the
original data object by accessing each of the nodes independently with some
constant probability.

This paper considers secure network coding over networks with unequal link
capacities in the presence of a wiretapper that can wiretap any subset of k
links. Existing results show that for the case of equal (unit) link capacities,
the secrecy capacity is given by the cut-set bound, whether or not the location
of the wiretapped links is known, and can be achieved by injecting k random
keys at the source which are decoded at the sink along with the message.

Regenerating codes allow distributed storage systems to recover from the loss
of a storage node while transmitting the minimum possible amount of data across
the network. We present a systematic computer search for optimal systematic
regenerating codes. To search the space of potential codes, we reduce the
potential search space in several ways. We impose an additional symmetry
condition on codes that we consider.