Someone please explain what is the meaning of the words in shade
From Proof from the Book, 4th edition page 96:
Let $q$ be a prime power, set $n=4q-2$, and let
$Q = \{x \in \{+1,-1\}^n: x_1 = 1, \#\{i:x_i=-1\} \text{ is even}\}.$
This $Q$ is a set of $2^{n-2}$ vectors in $\Bbb R^n$.
We will see that $\langle x,y \rangle \equiv 2 \pmod 4$ holds for all vectors $x,y \in Q$.
Remark: These 4 sentences came together.
And I need to understand what is $|\langle x,y \rangle|$ is in.
We will call $x,y$ nearly orthogonal if $|\langle x,y \rangle|=2$.