In all, a decent effort to explain an interesting technique. You appear to essentially be explaining a single a paper, which limits the amount by which you are able to build upon that work by synthesizing multiple works. You do convey some insight about what needs to change to eliminate false negatives, but presumably this is all in the Pagh paper. Your peer feedback said much the same, and you don't seem to have done much to address it.
There were many small English language problems.
Your claim in section 5 proof part 1 that there is always a (nonzero) solution to your linear system involving M is only true if the rows of M are linearly independent. Which happens with high probability but not certainty. If you rely on it, then in part 2 you have to show that the probability of a collision is small *even conditioning on the linear independence*.
These methods seem highly specialized to Hamming distance. What can we say going beyond 0-1 vectors and the L1 norm? Euclidean metric for example?
The use of specific numbers in your example on pages 4-5 makes it hard to see what is going on asumptotically.
Grade: B