  A modified $k$-deck of a graph $G$ is obtained by removing $k$ edges of $G$
in all possible ways, and adding $k$ (not necessarily new) edges in all
possible ways. Krasikov and Roditty asked if it was possible to construct the
usual $k$-edge deck of a graph from its modified $k$-deck. Earlier I solved
this problem for the case when $k=1$. In this paper, the problem is completely
solved for arbitrary $k$. The proof makes use of the $k$-edge version of
Lov\'asz's result and the eigenvalues of certain matrix related to the Johnson
graph.
  This version differs from the published version. Lemma 2.3 in the published
version had a typo in one equation. Also, a long manipulation of some
combinatorial expressions was skipped in the original proof of Lemma 2.3, which
made it difficult to follow the proof. Here a clearer proof is given.
