A-6.3 Approximate Decomposition

If the base $\beta$ does not divide the modulo $q$, then there exists no level $l$ such that ${\beta }^l|q$, thus some lower bits of $q$ have to be drawn away during decomposition, as shown in Figure 2. Such lower bits can be rounded to the nearest multiple of ${\displaystyle \frac{q}{{\beta }^l}}$ during decomposition. In such a case, the decomposition is an approximate decomposition.