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- W4297492736 abstract "In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, 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 possible linearity of $2^5$ (that is, minimum possible nonlinearity $2^4$). In this article, we show that the case of $n leq 5$ is quite special in the sense that Gold APN functions in dimension $n>5$ cannot be extended to quadratic APN functions in dimension $n+1$ having maximum possible linearity. In the second part of this work, we show that this is also the case for APN functions of the form $x mapsto x^3 + mu(x)$ with $mu$ being a quadratic Boolean function." @default.
- W4297492736 created "2022-09-29" @default.
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- W4297492736 date "2022-09-28" @default.
- W4297492736 modified "2023-09-26" @default.
- W4297492736 title "Gold functions and switched cube functions are not 0-extendable in dimension n > 5" @default.
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- W4297492736 doi "https://doi.org/10.1007/s10623-022-01111-6" @default.
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