Originally Posted by

**Migotek84** We are working in GF(2). Consider following polynomial:

$\displaystyle

A: x_1+x_2+1=0

$

Now multiply it by all monomials, that mean $\displaystyle x_1, x_2, x_3, x_4$ to get:

$\displaystyle

A_1: x_1x_2=0

$

$\displaystyle

A_2: x_1x_3+x_2x_3+x_3=0

$

$\displaystyle

A_3: x_2x_4+x_2x_4+x_4=0

$

I know that $\displaystyle A_2:=A*x_3, A_3:=A*x_4$ but from where we have $\displaystyle A_1$? We should multiply $\displaystyle A$ by $\displaystyle x_1$ and then by $\displaystyle x_2$. From this two new equations we have $\displaystyle A_1$ but how we could get it?