I am currently reading a research paper that uses the term 2-flat. However, I don't understand what this term means.
For example, the paper mentions in its definition of APN that for all distinct $a$, $b$, $c$ and $d$ in $V$,
$$a + b + c + d = 0 \implies f(a) + f(b) + f(c) + f(d) \neq 0$$
i.e. $f$ does not sum to 0 on any 2-flat.
It would be great if anyone could explain what 2-flat means here.