when 31 is divided by 16, Why the result of round is -2

Hello @yyf

It’s a matter of modular reduction, if you see in the beginning of the post we defined polynomials like this:

if we do the division we end up with a first coefficient equal to 2, but as 31 \equiv -33 \mod(64), it’s the same as -2 if we want to stick with coefficients in {-2, -1, 0, 1}.