Counting all bent functions in dimension eight 99270589265934370305785861242880
Counting all bent functions in dimension eight 99270589265934370305785861242880
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DOI：
10.1007/s10623-010-9455-z
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
Philippe Langevin;G. Leander
中科院分区：
文献类型：
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作者：
Philippe Langevin;G. Leander
在对8元4次齐次布尔函数进行分类的基础上，给出了计算所有8维Bent函数个数的策略，共$99270589265934370305785861242880\约2^{106}$$。此外，我们还证明了大多数8维Bent函数与Maiorana-McFarland函数和部分扩展函数不等价。
Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are $$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.