Research Article
Classification of Boolean Functions Where Affine Functions Are Uniformly Distributed
(a) |
| XOR | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 |
| 0 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 2 | 2 | 0 | 6 | 4 | 10 | 8 | 14 | 12 | 34 | 32 | 38 | 36 | 42 | 40 | 46 | 44 | 4 | 4 | 6 | 0 | 2 | 12 | 14 | 8 | 10 | 36 | 38 | 32 | 34 | 44 | 46 | 40 | 42 | 6 | 6 | 4 | 2 | 0 | 14 | 12 | 10 | 8 | 38 | 36 | 34 | 32 | 46 | 44 | 42 | 40 | 8 | 8 | 10 | 12 | 14 | 0 | 2 | 4 | 6 | 40 | 42 | 44 | 46 | 32 | 34 | 36 | 38 | 10 | 10 | 8 | 14 | 12 | 2 | 0 | 6 | 4 | 42 | 40 | 46 | 44 | 34 | 32 | 38 | 36 | 12 | 12 | 14 | 8 | 10 | 4 | 6 | 0 | 2 | 44 | 46 | 40 | 42 | 36 | 38 | 32 | 34 | 14 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 0 | 46 | 44 | 42 | 40 | 38 | 36 | 34 | 32 | 32 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 34 | 34 | 32 | 38 | 36 | 42 | 40 | 46 | 44 | 2 | 0 | 6 | 4 | 10 | 8 | 14 | 12 | 36 | 36 | 38 | 32 | 34 | 44 | 46 | 40 | 42 | 4 | 6 | 0 | 2 | 12 | 14 | 8 | 10 | 38 | 38 | 36 | 34 | 32 | 46 | 44 | 42 | 40 | 6 | 4 | 2 | 0 | 14 | 12 | 10 | 8 | 40 | 40 | 42 | 44 | 46 | 32 | 34 | 36 | 38 | 8 | 10 | 12 | 14 | 0 | 2 | 4 | 6 | 42 | 42 | 40 | 46 | 44 | 34 | 32 | 38 | 36 | 10 | 8 | 14 | 12 | 2 | 0 | 6 | 4 | 44 | 44 | 46 | 40 | 42 | 36 | 38 | 32 | 34 | 12 | 14 | 8 | 10 | 4 | 6 | 0 | 2 | 46 | 46 | 44 | 42 | 40 | 38 | 36 | 34 | 32 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 0 |
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(b) |
| XOR | 128 | 130 | 132 | 134 | 136 | 138 | 140 | 142 | 160 | 162 | 164 | 166 | 168 | 170 | 172 | 174 |
| 128 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 130 | 2 | 0 | 6 | 4 | 10 | 8 | 14 | 12 | 34 | 32 | 38 | 36 | 42 | 40 | 46 | 44 | 132 | 4 | 6 | 0 | 2 | 12 | 14 | 8 | 10 | 36 | 38 | 32 | 34 | 44 | 46 | 40 | 42 | 134 | 6 | 4 | 2 | 0 | 14 | 12 | 10 | 8 | 38 | 36 | 34 | 32 | 46 | 44 | 42 | 40 | 136 | 8 | 10 | 12 | 14 | 0 | 2 | 4 | 6 | 40 | 42 | 44 | 46 | 32 | 34 | 36 | 38 | 138 | 10 | 8 | 14 | 12 | 2 | 0 | 6 | 4 | 42 | 40 | 46 | 44 | 34 | 32 | 38 | 36 | 140 | 12 | 14 | 8 | 10 | 4 | 6 | 0 | 2 | 44 | 46 | 40 | 42 | 36 | 38 | 32 | 34 | 142 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 0 | 46 | 44 | 42 | 40 | 38 | 36 | 34 | 32 | 160 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 162 | 34 | 32 | 38 | 36 | 42 | 40 | 46 | 44 | 2 | 0 | 6 | 4 | 10 | 8 | 14 | 12 | 164 | 36 | 38 | 32 | 34 | 44 | 46 | 40 | 42 | 4 | 6 | 0 | 2 | 12 | 14 | 8 | 10 | 166 | 38 | 36 | 34 | 32 | 46 | 44 | 42 | 40 | 6 | 4 | 2 | 0 | 14 | 12 | 10 | 8 | 168 | 40 | 42 | 44 | 46 | 32 | 34 | 36 | 38 | 8 | 10 | 12 | 14 | 0 | 2 | 4 | 6 | 170 | 42 | 40 | 46 | 44 | 34 | 32 | 38 | 36 | 10 | 8 | 14 | 12 | 2 | 0 | 6 | 4 | 172 | 44 | 46 | 40 | 42 | 36 | 38 | 32 | 34 | 12 | 14 | 8 | 10 | 4 | 6 | 0 | 2 | 174 | 46 | 44 | 42 | 40 | 38 | 36 | 34 | 32 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 0 |
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(c) |
| XOR | 192 | 194 | 196 | 198 | 200 | 202 | 204 | 206 | 224 | 226 | 228 | 230 | 232 | 234 | 236 | 238 |
| 192 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 194 | 2 | 0 | 6 | 4 | 10 | 8 | 14 | 12 | 34 | 32 | 38 | 36 | 42 | 40 | 46 | 44 | 196 | 4 | 6 | 0 | 2 | 12 | 14 | 8 | 10 | 36 | 38 | 32 | 34 | 44 | 46 | 40 | 42 | 198 | 6 | 4 | 2 | 0 | 14 | 12 | 10 | 8 | 38 | 36 | 34 | 32 | 46 | 44 | 42 | 40 | 200 | 8 | 10 | 12 | 14 | 0 | 2 | 4 | 6 | 40 | 42 | 44 | 46 | 32 | 34 | 36 | 38 | 202 | 10 | 8 | 14 | 12 | 2 | 0 | 6 | 4 | 42 | 40 | 46 | 44 | 34 | 32 | 38 | 36 | 204 | 12 | 14 | 8 | 10 | 4 | 6 | 0 | 2 | 44 | 46 | 40 | 42 | 36 | 38 | 32 | 34 | 206 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 0 | 46 | 44 | 42 | 40 | 38 | 36 | 34 | 32 | 224 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 226 | 34 | 32 | 38 | 36 | 42 | 40 | 46 | 44 | 2 | 0 | 6 | 4 | 10 | 8 | 14 | 12 | 228 | 36 | 38 | 32 | 34 | 44 | 46 | 40 | 42 | 4 | 6 | 0 | 2 | 12 | 14 | 8 | 10 | 230 | 38 | 36 | 34 | 32 | 46 | 44 | 42 | 40 | 6 | 4 | 2 | 0 | 14 | 12 | 10 | 8 | 232 | 40 | 42 | 44 | 46 | 32 | 34 | 36 | 38 | 8 | 10 | 12 | 14 | 0 | 2 | 4 | 6 | 234 | 42 | 40 | 46 | 44 | 34 | 32 | 38 | 36 | 10 | 8 | 14 | 12 | 2 | 0 | 6 | 4 | 236 | 44 | 46 | 40 | 42 | 36 | 38 | 32 | 34 | 12 | 14 | 8 | 10 | 4 | 6 | 0 | 2 | 138 | 46 | 44 | 42 | 40 | 38 | 36 | 34 | 32 | 14 | 12 | 10 | 8 | 6 | 4 | 2 | 0 |
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