This thesis deals with the problem of code design in the setting of distributed storage systems consisting of multiple storage nodes, storing many different data les. A primary goal in such systems is the efficient repair ...

The projective space $\mathbb{P}_q(n)$ of order $n$ over a finite field $\mathbb{F}_q$ is defined as the collection of all subspaces of the ambient space $\mathbb{F}_q^n$. The Grassmannian $\mathcal{G}_q(n, k)$ is the set ...