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 (n,k) 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 channel condition characterized by packet erasure probability. Then, we introduce another important performance metric called minimum latency, 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.