  This paper addresses the gradient coding and coded matrix multiplication
problems in distributed optimization and coded computing. We present a
numerically stable binary coding method which overcomes the drawbacks of the
\textit{Fractional Repetition Coding} gradient coding method proposed by Tandon
et al., and can also be leveraged by coded computing networks whose servers are
of heterogeneous nature. Specifically, we propose a construction for fractional
repetition gradient coding; while ensuring that the generator matrix remains
close to perfectly balanced for any set of coded parameters, as well as a low
complexity decoding step. The proposed binary encoding avoids operations over
the real and complex numbers which are inherently numerically unstable, thereby
enabling numerically stable distributed encodings of the partial gradients. We
then make connections between gradient coding and coded matrix multiplication.
Specifically, we show that any gradient coding scheme can be extended to coded
matrix multiplication. Furthermore, we show how the proposed binary gradient
coding scheme can be used to construct two different coded matrix
multiplication schemes, each achieving different trade-offs.
