Technology has grown over the years, resulting
in more stress on data storage servers. As
the years goes by the data files size also grow,
resulting in bigger files than a server can handle.
In case the server crashes the data file is
lost. Hence data distribution storage (DDS)
systems are initiated, meaning the file is distributed
across multiple servers. This indicated
that error-correction codes could be
used, as if one server crashes it can be reconstructed.
However, for error-correction
algorithms they reconstruct the entire codeword
instead of the one broken entry. This
is related to the exact repair problem (ERP)
where this thesis will study the ERP for Reed-
Solomon (RS) codes over extension fields. If
the data is distributed as a RS codeword,
then by solving the ERP then any data on a
crashed server can be restored. This process
is called a linear exact repair scheme. The
approach in this project will combine Galois
theory, coding theory and linear algebra to
create an optimal repair scheme.