  We consider the problem of coded distributed computing where a large linear
computational job, such as a matrix multiplication, is divided into $k$ smaller
tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed
nodes. The goal is to reduce the average execution time of the computational
job. We provide a connection between the problem of characterizing the average
execution time of a coded distributed computing system and the problem of
analyzing the error probability of codes of length $n$ used over erasure
channels. Accordingly, we present closed-form expressions for the execution
time using binary random linear codes and the best execution time any
linear-coded distributed computing system can achieve. It is also shown that
there exist good binary linear codes that attain, asymptotically, the best
performance any linear code, not necessarily binary, can achieve. We also
investigate the performance of coded distributed computing systems using polar
and Reed-Muller (RM) codes that can benefit from low-complexity decoding, and
superior performance, respectively, as well as explicit constructions. The
proposed framework in this paper can enable efficient designs of distributed
computing systems given the rich literature in the channel coding theory.
