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

Gold Functions and Switched Cube Functions Are Not 0-Extendable in Dimension $n > 5$