  An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is
studied. It is proved that over any erasure channel (with or without memory),
Maximum Distance Separable (MDS) codes achieve the minimum probability of error
(assuming maximum likelihood decoding). Assuming a memoryless erasure channel,
the error exponent of MDS codes are compared with that of random codes and
linear random codes. It is shown that the envelopes of all these exponents are
identical for rates above the critical rate. Noting the optimality of MDS
codes, it is concluded that both random codes and linear random codes are
exponentially optimal, whether the block sizes is larger or smaller than the
alphabet size.
