In Alexander May's Paper "How to Meet Ternary LWE Keys", Alexander May writes the following about combining representation techniques with Odlyzko's locality sensitive hash function (Page 12):
Intuitively, in a subset sum-type approach of the representation technique as
in [HJ10], one would try to construct two lists $L_1$, $L_2$ with entries $(s_1, \ell(As_1)),
(s_2, \ell(b − As_2))$ recursively such that on expectation $L_1 \times L_2$ contains a single
representation. However, the non-linearity of Odlyzko’s hash function hinders
such a direct recursive application of the representation technique.
I am trying to get a more solid understanding on why that is. If I understand correctly, a recursive application would try to split up the $s_1$ and $s_2$ even further (using again the representation technique) into another $s_1 = s^{(2)}_1 + s^{(2)}_2$ and then filter out representations such that, in expectation, one correct representation of $s_1$ and $s_2$ remains. It is however not so clear to me how exactly one would go about such a recursive construction and why it is prevented by the non-linearity of the locality sensitive hash function?
