Consider [bipartite graph][1].
Consider its [incidence matrix][2].
It will have a form 

0 A^t

A 0

Take matrix $A$. 
Consider the null-space $L$ of $A$ over $F_2^N$.

**Question** Can we say something about the $L$ from graph theoretic perspective ?
For example to determine what is minimum [Hamming weight][5] for vectors in $L$ ?

In error correction codes community the following words are used:
Original graph is called [Tanner graph][3] for $A$.
Matrix $A$ is called [parity-check matrix][4].
Let dim(L)=k, any linear map $F_2^k \to L\subset F_2^N$ is called "encoder".


  [1]: http://en.wikipedia.org/wiki/Bipartite_graph
  [2]: http://en.wikipedia.org/wiki/Incidence_matrix
  [3]: http://en.wikipedia.org/wiki/Tanner_graph
  [4]: http://en.wikipedia.org/wiki/Parity-check_matrix
  [5]: http://en.wikipedia.org/wiki/Hamming_weight