  A generic $(r,m)$-erasure correcting set is a collection of vectors in
$\bF_2^r$ which can be used to generate, for each binary linear code of
codimension $r$, a collection of parity check equations that enables iterative
decoding of all correctable erasure patterns of size at most $m$.
  That is to say, the only stopping sets of size at most $m$ for the generated
parity check equations are the erasure patterns for which there is more than
one manner to fill in theerasures to obtain a codeword.
  We give an explicit construction of generic $(r,m)$-erasure correcting sets
of cardinality $\sum_{i=0}^{m-1} {r-1\choose i}$. Using a random-coding-like
argument, we show that for fixed $m$, the minimum size of a generic
$(r,m)$-erasure correcting set is linear in $r$.
  Keywords: iterative decoding, binary erasure channel, stopping set
