Research Article
Classification of Boolean Functions Where Affine Functions Are Uniformly Distributed
| | Class 1 |
| | BF | DV | HD | No. of BF |
| | 00000000 | 0 | 0 | 1 |
| | 00000010 | 2 | 1 | 4 | | 00100000 | 32 | | 00001000 | 8 | | 00000100 | 4 |
| | 00100010 | 34 | 2 | 6 | | 00001010 | 10 | | 00101000 | 40 | | 00001100 | 12 | | 00000110 | 6 | | 00100100 | 36 |
| | 00101010 | 42 | 3 | 4 | | 00001110 | 14 | | 00101100 | 44 | | 00100110 | 38 |
| | 00101110 | 46 | 4 | 1 |
| | Class 2 |
| | BF | DV | HD | No. of BF |
| | 10101010 | 170 | 0 | 1 |
| | 10100010 | 162 | 1 | 4 | | 10101000 | 168 | | 10001010 | 138 | | 10101110 | 174 |
| | 10100000 | 160 | 2 | 6 | | 10000010 | 130 | | 10001000 | 136 | | 10101100 | 172 | | 10001110 | 142 | | 10100110 | 166 |
| | 10000000 | 128 | 3 | 4 | | 10001100 | 140 | | 10100100 | 164 | | 10000110 | 134 |
| | 10000100 | 132 | 4 | 1 |
| | Class 3 |
| | BF | DV | HD | No. of BF |
| | 11001100 | 204 | 0 | 1 |
| | 11001000 | 200 | 1 | 4 | | 11001110 | 206 | | 11101100 | 236 | | 11000100 | 196 |
| | 11000000 | 192 | 2 | 6 | | 11001010 | 202 | | 11101000 | 232 | | 11101110 | 238 | | 11000110 | 198 | | 11100100 | 228 |
| | 11000010 | 194 | 3 | 4 | | 11100000 | 224 | | 11101010 | 234 | | 11100110 | 230 |
| | 11100010 | 226 | 4 | 1 |
| | Class 4 |
| | BF | DV | HD | No. of BF |
| | 01100110 | 102 | 0 | 1 |
| | 01100010 | 98 | 1 | 4 | | 01101110 | 110 | | 01100100 | 100 | | 01000110 | 70 |
| | 01100000 | 96 | 2 | 6 | | 01000010 | 66 | | 01101010 | 106 | | 01101100 | 108 | | 01001110 | 78 | | 01000100 | 68 |
| | 01000000 | 64 | 3 | 4 | | 01101000 | 104 | | 01001010 | 74 | | 01001100 | 76 |
| | 01001000 | 72 | 4 | 1 |
| | Class 5 |
| | BF | DV | HD | No. of BF |
| | 11110000 | 240 | 0 | 1 |
| | 11110010 | 242 | 1 | 4 | | 11010000 | 208 | | 11111000 | 248 | | 11110100 | 244 |
| | 11010010 | 210 | 2 | 6 | | 11111010 | 250 | | 11011000 | 216 | | 11111100 | 252 | | 11110110 | 246 | | 11010100 | 212 |
| | 11011010 | 218 | 3 | 4 | | 11111110 | 254 | | 11011100 | 220 | | 11010110 | 214 |
| | 11011110 | 222 | 4 | 1 |
| | Class 6 |
| | BF | DV | HD | No. of BF |
| | 01011010 | 90 | 0 | 1 |
| | 01010010 | 82 | 1 | 4 | | 01011000 | 88 | | 01111010 | 122 | | 01011110 | 94 |
| | 01010000 | 80 | 2 | 6 | | 01110010 | 114 | | 01111000 | 120 | | 01011100 | 92 | | 01111110 | 126 | | 01010110 | 86 |
| | 01110000 | 112 | 3 | 4 | | 01111100 | 124 | | 01010100 | 84 | | 01110110 | 118 |
| | 01110100 | 116 | 4 | 1 |
| | Class 7 |
| | BF | DV | HD | No. of BF |
| | 00111100 | 60 | 0 | 1 |
| | 00111000 | 56 | 1 | 4 | | 00111110 | 62 | | 00011100 | 28 | | 00110100 | 52 |
| | 00110000 | 48 | 2 | 6 | | 00111010 | 58 | | 00011000 | 24 | | 00011110 | 30 | | 00110110 | 54 | | 00010100 | 20 |
| | 00110010 | 50 | 3 | 4 | | 00010000 | 16 | | 00011010 | 26 | | 00010110 | 22 |
| | 00010010 | 18 | 4 | 1 |
| | Class 8 |
| | BF | DV | HD | No. of BF |
| | 10010110 | 150 | 0 | 1 |
| | 10010010 | 146 | 1 | 4 | | 10011110 | 158 | | 10010100 | 148 | | 10110110 | 182 |
| | 10010000 | 144 | 2 | 6 | | 10110010 | 178 | | 10011010 | 154 | | 10011100 | 156 | | 10111110 | 190 | | 10110100 | 180 |
| | 10110000 | 176 | 3 | 4 | | 10011000 | 152 | | 10111010 | 186 | | 10111100 | 188 |
| | 10111000 | 184 | 4 | 1 |
| | Class 9 |
| | BF | DV | HD | No. of BF |
| | 11111111 | 255 | 0 | 1 |
| | 11111101 | 253 | 1 | 4 | | 11011111 | 223 | | 11110111 | 247 | | 11111011 | 251 |
| | 11011101 | 221 | 2 | 6 | | 11110101 | 245 | | 11010111 | 215 | | 11110011 | 243 | | 11111001 | 249 | | 11011011 | 219 |
| | 11010101 | 213 | 3 | 4 | | 11110001 | 241 | | 11010011 | 211 | | 11011001 | 217 |
| | 11010001 | 209 | 4 | 1 |
| | Class 10 |
| | BF | DV | HD | No. of BF |
| | 01010101 | 85 | 0 | 1 |
| | 01011101 | 93 | 1 | 4 | | 01010111 | 87 | | 01110101 | 117 | | 01010001 | 81 |
| | 01011111 | 95 | 2 | 6 | | 01111101 | 125 | | 01110111 | 119 | | 01010011 | 83 | | 01110001 | 113 | | 01011001 | 89 |
| | 01111111 | 127 | 3 | 4 | | 01110011 | 115 | | 01011011 | 91 | | 01111001 | 121 |
| | 01111011 | 123 | 4 | 1 |
| | Class 11 |
| | BF | DV | HD | No. of BF |
| | 00110011 | 51 | 0 | 1 |
| | 00110111 | 55 | 1 | 4 | | 00110001 | 49 | | 00010011 | 19 | | 00111011 | 59 |
| | 00111111 | 63 | 2 | 6 | | 00110101 | 53 | | 00010111 | 23 | | 00010001 | 17 | | 00111001 | 57 | | 00011011 | 27 |
| | 00111101 | 61 | 3 | 4 | | 00011111 | 31 | | 00010101 | 21 | | 00011001 | 25 |
| | 00011101 | 29 | 4 | 1 |
| | Class 12 |
| | BF | DV | HD | No. of BF |
| | 10011001 | 153 | 0 | 1 |
| | 10011101 | 157 | 1 | 4 | | 10010001 | 145 | | 10011011 | 155 | | 10111001 | 185 |
| | 10011111 | 159 | 2 | 6 | | 10111101 | 189 | | 10010101 | 149 | | 10010011 | 147 | | 10110001 | 177 | | 10111011 | 187 |
| | 10111111 | 191 | 3 | 4 | | 10010111 | 151 | | 10110101 | 181 | | 10110011 | 179 |
| | 10110111 | 183 | 4 | 1 |
| | Class 13 |
| | BF | DV | HD | No. of BF |
| | 00001111 | 15 | 0 | 1 |
| | 00001101 | 13 | 1 | 4 | | 00101111 | 47 | | 00000111 | 7 | | 00001011 | 11 |
| | 00101101 | 45 | 2 | 6 | | 00000101 | 5 | | 00100111 | 39 | | 00000011 | 3 | | 00001001 | 9 | | 00101011 | 43 |
| | 00100101 | 37 | 3 | 4 | | 00000001 | 1 | | 00100011 | 35 | | 00101001 | 41 |
| | 00100001 | 33 | 4 | 1 |
| | Class 14 |
| | BF | DV | HD | No. of BF |
| | 10100101 | 165 | 0 | 1 |
| | 10101101 | 173 | 1 | 4 | | 10100111 | 167 | | 10000101 | 133 | | 10100001 | 161 |
| | 10101111 | 175 | 2 | 6 | | 10001101 | 141 | | 10000111 | 135 | | 10100011 | 163 | | 10000001 | 129 | | 10101001 | 169 |
| | 10001111 | 143 | 3 | 4 | | 10000011 | 131 | | 10101011 | 171 | | 10001001 | 137 |
| | 10001011 | 139 | 4 | 1 |
| | Class 15 |
| | BF | DV | HD | No. of BF |
| | 11000011 | 195 | 0 | 1 |
| | 11000111 | 199 | 1 | 4 | | 11000001 | 193 | | 11100011 | 227 | | 11001011 | 203 |
| | 11001111 | 207 | 2 | 6 | | 11000101 | 197 | | 11100111 | 231 | | 11100001 | 225 | | 11001001 | 201 | | 11101011 | 235 |
| | 11001101 | 205 | 3 | 4 | | 11101111 | 239 | | 11100101 | 229 | | 11101001 | 233 |
| | 11101101 | 237 | 4 | 1 |
| | Class 16 |
| | BF | DV | HD | No. of BF |
| | 01101001 | 105 | 0 | 1 |
| | 01101101 | 109 | 1 | 4 | | 01100001 | 97 | | 01101011 | 107 | | 01001001 | 73 |
| | 01101111 | 111 | 2 | 6 | | 01001101 | 77 | | 01100101 | 101 | | 01100011 | 99 | | 01000001 | 65 | | 01001011 | 75 |
| | 01001111 | 79 | 3 | 4 | | 01100111 | 103 | | 01000101 | 69 | | 01000011 | 67 |
| | 01000111 | 71 | 4 | 1 |
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BF: Boolean function, DV: decimal value, HD: Hamming distance, and No. BF: number of Boolean functions.
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