  Let C = {x_1,...,x_N} \subset {0,1}^n be an [n,N] binary error correcting
code (not necessarily linear). Let e \in {0,1}^n be an error vector. A codeword
x in C is said to be "disturbed" by the error e if the closest codeword to x +
e is no longer x. Let A_e be the subset of codewords in C that are disturbed by
e. In this work we study the size of A_e in random codes C (i.e. codes in which
each codeword x_i is chosen uniformly and independently at random from
{0,1}^n). Using recent results of Vu [Random Structures and Algorithms 20(3)]
on the concentration of non-Lipschitz functions, we show that |A_e| is strongly
concentrated for a wide range of values of N and ||e||.
  We apply this result in the study of communication channels we refer to as
"oblivious". Roughly speaking, a channel W(y|x) is said to be oblivious if the
error distribution imposed by the channel is independent of the transmitted
codeword x. For example, the well studied Binary Symmetric Channel is an
oblivious channel.
  In this work, we define oblivious and partially oblivious channels and
present lower bounds on their capacity. The oblivious channels we define have
connections to Arbitrarily Varying Channels with state constraints.
