Generating parity check equations for bounded-distance iterative erasure   decoding
  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 
Henk D.L. Hollmann and Ludo M.G.M. Tolhuizen