Thanks for the feedback! Roughly speaking, that all has to do with making e vanish later, so perhaps I need to revisit that section.
Quickly (cause I probably won't for a few days), (q//2)m can be seen as a form of error correction. You can check (either pen+paper or programmatically) that, provided |e| < q/4, if noisy_m = (q//2) m + e, then round(noisy_m / (q/4)) = m. So e vanishes because it is bounded (not uniform), + we encode m as (q//2)*m (i.e. in the "most significant bits" of the number).
Quickly (cause I probably won't for a few days), (q//2)m can be seen as a form of error correction. You can check (either pen+paper or programmatically) that, provided |e| < q/4, if noisy_m = (q//2) m + e, then round(noisy_m / (q/4)) = m. So e vanishes because it is bounded (not uniform), + we encode m as (q//2)*m (i.e. in the "most significant bits" of the number).