Gold functions and switched cube functions are not 0-extendable in dimension n > 5

Abstract In the independent works by Kalgin and Idrisova Beierle, Leander Perrin, it was observed that Gold APN functions over $$\mathbb {F}_{2^5}$$ F 2 5 give rise to a quadratic function in dimension 6 having maximum possible linearity of $$2^5$$ (that is, minimum nonlinearity $$2^4$$ 4 ). this article, we show case $$n \le 5$$ n ≤ is quite special sense $$n>5$$ > cannot be extended $$n+1$$ + 1 linearity. second part work, also for form $$x \mapsto x^3 + \mu (x)$$ x ↦ 3 μ ( ) with $$\mu $$ being Boolean function.