In wireless distributed computing systems, mobile devices that are connected wirelessly to the Fog (e.g., small base stations) collaboratively solve a given computational task. Unfortunately, wireless distributed computing systems suffer from packet losses due to severe channel fading. Moreover, a wireless device can drop out of the system when leaving the coverage of a master node in the Fog layer. We model this unreliability between a device and a master node as a packet erasure channel. When a packet fails to be detected at the receiver, the corresponding packet is retransmitted, which would significantly increase the overall run-time to finish the task. We take a coding-theoretic approach to tackle this straggler-like problem in wireless distributed computing. We first investigate the expected latency using an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n, k)$ </tex-math></inline-formula> maximum-distance separable (MDS) code. We obtain the lower and upper bounds on the latency in closed forms and provide guidelines to design MDS codes depending on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">channel</i> condition characterized by packet erasure probability. Then, we introduce another important performance metric called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">minimum latency</i> , and also provide guidelines on designing optimal codes. Based on optimal codes, we obtain the performance curves of achievable minimum latency and achievable workload as functions of packet erasure probability.