How to partition boolean functions into CCZ(Carlet-Charpin-Zinovlev) equivalent classes

Question

I'm doing some exercises for my course on Finite fields, and have a question regarding boolean functions.

The question gives me several (7,7) functions and asks me to partition them into CCZ equivalent classes (find all pairs among the given functions that are CCZ eqivalent).

The functions are:

f₁(x) = x¹⁰

f₂(x) = x²³

f₃(x) = x²⁵

f₄(x) = x⁴⁰

f₅(x) = x¹⁰¹

The problem I have is that I can't really find any examples on how this is done. Any pointers or guidance is appreciated!

Edit: CCZ stands Carlet-Charpin-Zinovlev equivalent. Two $(n, m)$-functions $F$ and $G$ are CCZ-equivalent if there is an affine permutation which maps the graph $\{(x, F(x)) : x \in \Bbb{F}_{2^n} \}$ of $F$ to the graph of $G$.