Boolf prop/3-ary/Zhegalkin deviation


The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.
But this is an exception for arity 3.



This is the XOR of Z.d. whose corresponding t.p. are n and ¬n.
Number of blocks: 16 Integer partition: 16⋅16
Explanation: Nonlinearity of Boolean functions#Zhegalkin deviation
| # | Zhegalkin deviation |
twin prefect |
block |
|---|---|---|---|
| 16 | 0 0 Ж 0 |
0, 0 0 |
[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]
|
| 16 | 232 104 Ж 232 |
0, 1 ¬0 |
[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]
|
| 16 | 168 168 Ж 168 |
1, 0 1 |
[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]
|
| 16 | 64 192 Ж 64 |
1, 1 ¬1 |
[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]
|
| 16 | 200 200 Ж 200 |
2, 0 2 |
[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]
|
| 16 | 32 160 Ж 32 |
2, 1 ¬2 |
[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]
|
| 16 | 96 96 Ж 96 |
3, 0 3 |
[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]
|
| 16 | 136 8 Ж 136 |
3, 1 ¬3 |
[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]
|
| 16 | 224 224 Ж 224 |
4, 0 4 |
[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]
|
| 16 | 8 136 Ж 8 |
4, 1 ¬4 |
[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]
|
| 16 | 72 72 Ж 72 |
5, 0 5 |
[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]
|
| 16 | 160 32 Ж 160 |
5, 1 ¬5 |
[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]
|
| 16 | 40 40 Ж 40 |
6, 0 6 |
[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]
|
| 16 | 192 64 Ж 192 |
6, 1 ¬6 |
[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]
|
| 16 | 128 128 Ж 128 |
7, 0 7 |
[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]
|
| 16 | 104 232 Ж 104 |
7, 1 ¬7 |
[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]
|















