I'm looking at different variants of Oddtown and I've come across the Mod 4 example online. However, in the PDF I was looking at, it said that the proof is wrong. However, I'm not sure where the mistake in the proof is. Could someone point me in the right direction to finding out the mistake in the proof?
Most of the proof is correct; the mistake is at the very end. When working modulo $4$, we cannot conclude from $\lambda_1 (v_1 \cdot v_1) \equiv 0$ and $v_1 \cdot v_1 \not\equiv 0$ that $\lambda_1 \equiv 0$.