How decode works in CCA1 scheme based on MP12 construction?
After some time I revisited the problem and found out that before decoding it is necessary to reduce modulo the fundamental region to find a coset, then we have that in the example I gave the internal value $2s+m$ is equal to $[1, 1, \dots]$, and after reduction it turns out to be equivalent to $[1, 0, \dots]$, which is $m$, as needed.