9 An Algorithm for Linear, Affine and Spectral Classification of Boolean Functions
207
Table 9.5 (continued)
Spectrum
Class (n = 4) f R
Count 0
1 2 3 4 12 13 23 14 24 34 123 124 134 234 1234
17
60,072
1920
0 12 4 4 4
0
0
0
0
0
0 −4 −4 −4
4
0
18
60,074
240
−2 14 2 2 2
2
2 −2
2 −2 −2 −2 −2 −2
2
2
19
60,104 10,080
0 8 8 4 4
0
4 −4 −4
4
0 −4 −4
0
0
0
20
60,136
6720
−2 10 6 6 2
2
2 −2 −2
2
2 −6 −2 −2
2 −2
21
60,138
840
−4 12 4 4 0
4
4 −4
0
0
0 −4
0
0
0
0
22
61,152
4480
−2 6 6 6 6
6 −2 −2 −2 −2
6 −2 −2 −2 −2 −2
23
61,160
6720
−4 8 8 4 4
4
0
0
0
0
4 −4 −4
0
0 −4
24
61,162
1680
−6 10 6 2 2
6
2 −2
2 −2
2 −2 −2
2 −2 −2
25
61,166
140
−8 8 8 0 0
8
0
0
0
0
0
0
0
0
0
0
26
63,624
4480
2 6 6 6 6 −6
2
2
2
2 −6 −2 −2 −2 −2
2
27
65,256
2688
−6 6 6 6 6
2
2
2
2
2
2 −2 −2 −2 −2 −6
28
65,258
1680
−8 8 4 4 4
4
4
0
4
0
0
0
0
0 −4 −4
29
65,262
560 −10 6 6 2 2
6
2
2
2
2 −2
2
2 −2 −2 −2
30
65,278
120 −12 4 4 4 0
4
4
4
0
0
0
4
0
0
0
0
31
65,534
16 −14 2 2 2 2
2
2
2
2
2
2
2
2
2
2
2
32
65,535
1 −16 0 0 0 0
0
0
0
0
0
0
0
0
0
0
0
Table 9.6 Spectral equivalence classes n = 1, 2, 3, 4
Spectrum
Class (n = 1)
f R
Count
0
1
1
0
4
2
0
Spectrum
Class (n = 2)
f R
Count
0
1
2
12
1
0
8
4
0
0
0
2
8
8
2
2
2
−2
Spectrum
Class (n = 3)
f R
Count
0
1
2
3
12
13
23
123
1
0
16
8
0
0
0
0
0
0
0
2
128
128
6
2
2
2
−2
−2
−2
2
3
136
112
4
4
4
0
−4
0
0
0
Spectrum
Class (n = 4) f R
Count
0 1 2 3 4 12 13 23 14 24 34 123 124 134 234 1234
1
0
32 16 0 0 0 0 0
0
0
0
0
0
0
0
0
0
0
2
27,328
896 4 4 4 4 4 4
4 −4 −4
4
4 −4 −4 −4 −4
4
3
32,768
512 14 2 2 2 2 −2 −2 −2 −2 −2 −2
2
2
2
2 −2
4
32,896
3840 12 4 4 4 0 −4 −4 −4
0
0
0
4
0
0
0
0
5
34,944 17,920 10 6 6 2 2 −6 −2 −2 −2 −2
2
2
2 −2 −2
2
6
34,952
1120 8 8 8 0 0 −8
0
0
0
0
0
0
0
0
0
0
7
43,136 26,880 8 8 4 4 4 −4 −4
0 −4
0
0
0
0
0 −4
4
8
59,520 14,336 6 6 6 6 6 −2 −2 −2 −2 −2 −2 −2 −2 −2 −2
6