  We prove the following results concerning the list decoding of
error-correcting codes:
  (i) We show that for \textit{any} code with a relative distance of $\delta$
(over a large enough alphabet), the following result holds for \textit{random
errors}: With high probability, for a $\rho\le \delta -\eps$ fraction of random
errors (for any $\eps>0$), the received word will have only the transmitted
codeword in a Hamming ball of radius $\rho$ around it. Thus, for random errors,
one can correct twice the number of errors uniquely correctable from worst-case
errors for any code. A variant of our result also gives a simple algorithm to
decode Reed-Solomon codes from random errors that, to the best of our
knowledge, runs faster than known algorithms for certain ranges of parameters.
  (ii) We show that concatenated codes can achieve the list decoding capacity
for erasures. A similar result for worst-case errors was proven by Guruswami
and Rudra (SODA 08), although their result does not directly imply our result.
Our results show that a subset of the random ensemble of codes considered by
Guruswami and Rudra also achieve the list decoding capacity for erasures.
  Our proofs employ simple counting and probabilistic arguments.
