  Locally repairable codes (LRCs) are error correcting codes used in
distributed data storage. A traditional approach is to look for codes which
simultaneously maximize error tolerance and minimize storage space consumption.
However, this tends to yield codes for which error correction requires an
unrealistic amount of communication between storage nodes. LRCs solve this
problem by allowing errors to be corrected locally.
  This thesis reviews previous results on the subject presented in [1]. These
include that every almost affine LRC induces a matroid such that the essential
properties of the code are determined by the matroid. Also, the generalized
Singleton bound for LRCs can be extended to matroids as well. Then, matroid
theory can be used to find classes of matroids that either achieve the bound,
meaning they are optimal in a certain sense, or at least come close to the
bound. This thesis presents an improvement to the results of [1] in both of
these cases.
  [1] T. Westerb\"ack, R. Freij, T. Ernvall and C. Hollanti, "On the
Combinatorics of Locally Repairable Codes via Matroid Theory", arXiv:1501.00153
[cs.IT], 2014.
