It is well known that the performance of carrier sense multiple access with collision avoidance (CSMA/CA) is poor when the number of users increases, because of collisions. In this paper, we consider a modified version of CSMA/CA based on erasure codes at the packet level, which significantly reduces the complexity of the decoding and does not require any change in the underlying physical layer. In order to improve the performance we use non-binary maximum distance separable (MDS) codes. We give analytical derivation of the global goodput and show that there is a trade-off between the code parameters and the length of the contention window in order to maximize the global goodput for a given number of users.