I am following an academic lecture on coding theory. The following matrix multiplication is done at the lecture. I paste a clear screenshot of the frame below.
As stated on the figure, I do not understand how such a simplification (indicated by the red arrow) can be done. I would so much appreciate an elaborative answer which explains how this simplification. (the YouTube link opens the exact time he mentions this)
I truly appreciate for your valuable time.
Assuming the coefficients are mod 2,
\begin{align*} &v_0 = u_0 + u_2 + u_3\\[4pt] \implies\;&v_0 - u_0 - u_2 - u_3 = 0\\[4pt] \implies\;&v_0 + u_0 + u_2 + u_3 = 0\qquad\text{[since $-1 \equiv 1 \pmod 2$]}\\[4pt] \end{align*}