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The expression $c' = \lfloor w^{-i} c \rfloor$ is a slight abuse of notation. What it technically means is to interpret each coefficient of $c$ as real number, divide by $w^i$, round the result to the nearest integer, and then interpret it as an element of $\mathbb{Z}_q$ again. This is equivalent to expressing each $\mathbb{Z}_q$ coefficient of the ...

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