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Counting all bent functions in dimension eight 99270589265934370305785861242880

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Abstract

Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are

$$99270589265934370305785861242880 \approx 2^{106}$$

such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana–McFarland and partial spread functions.

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Correspondence to Philippe Langevin.

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Langevin, P., Leander, G. Counting all bent functions in dimension eight 99270589265934370305785861242880. Des. Codes Cryptogr. 59, 193–205 (2011). https://doi.org/10.1007/s10623-010-9455-z

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