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Counting all bent functions in dimension eight 99270589265934370305785861242880. (English) Zbl 1215.94059
Summary: 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.

94D10 Boolean functions
06E30 Boolean functions
65T50 Numerical methods for discrete and fast Fourier transforms
Full Text: DOI
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