CCZ-inequivalent representatives from the known APN families for dimensions up to 11: Difference between revisions
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Line 7: | Line 7: | ||
<th>Functions</th> | <th>Functions</th> | ||
<th>Equivalent to</th> | <th>Equivalent to</th> | ||
<th>Walsh spectrum</th> | |||
<th>Γ-rank</th> | |||
<th>Δ-rank</th> | |||
</tr> | </tr> | ||
Line 14: | Line 17: | ||
<td><math>x^3</math></td> | <td><math>x^3</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>1102</td> | |||
<td>94</td> | |||
</tr> | </tr> | ||
Line 21: | Line 27: | ||
<td><math>x^{24}+ax^{17}+a^8x^{10}+ax^9+x^3</math></td> | <td><math>x^{24}+ax^{17}+a^8x^{10}+ax^9+x^3</math></td> | ||
<td><math>C3</math></td> | <td><math>C3</math></td> | ||
<td>Gold</td> | |||
<td>1146</td> | |||
<td>94</td> | |||
</tr> | </tr> | ||
Line 27: | Line 36: | ||
<td><math>ax^3+x^{17}+a^4x^{24}</math></td> | <td><math>ax^3+x^{17}+a^4x^{24}</math></td> | ||
<td><math>C7-C9</math></td> | <td><math>C7-C9</math></td> | ||
<td>Gold</td> | |||
<td>1166</td> | |||
<td>96</td> | |||
</tr> | </tr> | ||
Line 35: | Line 47: | ||
<td><math>x^3</math></td> | <td><math>x^3</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>3610</td> | |||
<td>198</td> | |||
</tr> | </tr> | ||
Line 42: | Line 57: | ||
<td><math>x^5</math></td> | <td><math>x^5</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>3708</td> | |||
<td>198</td> | |||
</tr> | </tr> | ||
Line 49: | Line 67: | ||
<td><math>x^9</math></td> | <td><math>x^9</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>3610</td> | |||
<td>198</td> | |||
</tr> | </tr> | ||
Line 56: | Line 77: | ||
<td><math>x^{13}</math></td> | <td><math>x^{13}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td>4270</td> | |||
<td>338</td> | |||
</tr> | </tr> | ||
Line 62: | Line 86: | ||
<td><math>x^{57}</math></td> | <td><math>x^{57}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td>4704</td> | |||
<td>436</td> | |||
</tr> | </tr> | ||
Line 69: | Line 96: | ||
<td><math>x^{63}</math></td> | <td><math>x^{63}</math></td> | ||
<td><math>Inverse</math></td> | <td><math>Inverse</math></td> | ||
<td>Inverse</td> | |||
<td>8128</td> | |||
<td>4928</td> | |||
</tr> | </tr> | ||
Line 77: | Line 107: | ||
<td><math>x^3+Tr_7(x^9)</math></td> | <td><math>x^3+Tr_7(x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td>4026</td> | |||
<td>212</td> | |||
</tr> | </tr> | ||
Line 85: | Line 118: | ||
<td><math>x^3</math></td> | <td><math>x^3</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>11818</td> | |||
<td>420</td> | |||
</tr> | </tr> | ||
Line 91: | Line 127: | ||
<td><math>x^9</math></td> | <td><math>x^9</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>12370</td> | |||
<td>420</td> | |||
</tr> | </tr> | ||
Line 98: | Line 137: | ||
<td><math>x^{57}</math></td> | <td><math>x^{57}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td>15358</td> | |||
<td>960</td> | |||
</tr> | </tr> | ||
Line 104: | Line 146: | ||
<td><math>x^3+x^{17}+p^{48}x^{18}+p^3x^{33}+px^{34}+x^{48}</math></td> | <td><math>x^3+x^{17}+p^{48}x^{18}+p^3x^{33}+px^{34}+x^{48}</math></td> | ||
<td><math>C3</math></td> | <td><math>C3</math></td> | ||
<td>Gold</td> | |||
<td>13200</td> | |||
<td>414</td> | |||
</tr> | </tr> | ||
Line 110: | Line 155: | ||
<td><math>x^3+Tr_8(x^9)</math></td> | <td><math>x^3+Tr_8(x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td>13200</td> | |||
<td>432</td> | |||
</tr> | </tr> | ||
Line 116: | Line 164: | ||
<td><math>x^3+a^{-1}Tr_8(a^3x^9)</math></td> | <td><math>x^3+a^{-1}Tr_8(a^3x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td>13842</td> | |||
<td>436</td> | |||
</tr> | </tr> | ||
Line 122: | Line 173: | ||
<td><math>a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12}</math></td> | <td><math>a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12}</math></td> | ||
<td><math>C10</math></td> | <td><math>C10</math></td> | ||
<td>Gold</td> | |||
<td>13642</td> | |||
<td>436</td> | |||
</tr> | </tr> | ||
Line 129: | Line 183: | ||
<td><math>x^3</math></td> | <td><math>x^3</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>38470</td> | |||
<td>872</td> | |||
</tr> | </tr> | ||
Line 136: | Line 193: | ||
<td><math>x^5</math></td> | <td><math>x^5</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>41494</td> | |||
<td>872</td> | |||
</tr> | </tr> | ||
Line 142: | Line 202: | ||
<td><math>x^{17}</math></td> | <td><math>x^{17}</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>38470</td> | |||
<td>872</td> | |||
</tr> | </tr> | ||
Line 148: | Line 211: | ||
<td><math>x^{13}</math></td> | <td><math>x^{13}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td>58676</td> | |||
<td>3086</td> | |||
</tr> | </tr> | ||
Line 154: | Line 220: | ||
<td><math>x^{241}</math></td> | <td><math>x^{241}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td>61726</td> | |||
<td>3482</td> | |||
</tr> | </tr> | ||
Line 160: | Line 229: | ||
<td><math>x^{19}</math></td> | <td><math>x^{19}</math></td> | ||
<td><math>Welch</math></td> | <td><math>Welch</math></td> | ||
<td>Gold</td> | |||
<td>60894</td> | |||
<td>3956</td> | |||
</tr> | </tr> | ||
Line 166: | Line 238: | ||
<td><math>x^{255}</math></td> | <td><math>x^{255}</math></td> | ||
<td><math>Inverse</math></td> | <td><math>Inverse</math></td> | ||
<td>Inverse</td> | |||
<td>130816</td> | |||
<td>93024</td> | |||
</tr> | </tr> | ||
Line 172: | Line 247: | ||
<td><math>x^3+Tr_9(x^9)</math></td> | <td><math>x^3+Tr_9(x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td>47890</td> | |||
<td>920</td> | |||
</tr> | </tr> | ||
Line 178: | Line 256: | ||
<td><math>x^3+Tr^3_9(x^9+x^{18})</math></td> | <td><math>x^3+Tr^3_9(x^9+x^{18})</math></td> | ||
<td><math>C5</math></td> | <td><math>C5</math></td> | ||
<td>Gold</td> | |||
<td>48428</td> | |||
<td>930</td> | |||
</tr> | </tr> | ||
Line 184: | Line 265: | ||
<td><math>x^3+Tr^3_9(x^{18}+x^{36})</math></td> | <td><math>x^3+Tr^3_9(x^{18}+x^{36})</math></td> | ||
<td><math>C6</math></td> | <td><math>C6</math></td> | ||
<td>Gold</td> | |||
<td>48460</td> | |||
<td>944</td> | |||
</tr> | </tr> | ||
Line 190: | Line 274: | ||
<td><math>x^3+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129}</math></td> | <td><math>x^3+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129}</math></td> | ||
<td><math>C11</math></td> | <td><math>C11</math></td> | ||
<td>Gold</td> | |||
<td>48596</td> | |||
<td>944</td> | |||
</tr> | </tr> | ||
Line 197: | Line 284: | ||
<td><math>x^3</math></td> | <td><math>x^3</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>125042</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 203: | Line 293: | ||
<td><math>x^9</math></td> | <td><math>x^9</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td>136492</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 209: | Line 302: | ||
<td><math>x^{57}</math></td> | <td><math>x^{57}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td>186416</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 215: | Line 311: | ||
<td><math>x^{339}</math></td> | <td><math>x^{339}</math></td> | ||
<td><math>Dobbertin</math></td> | <td><math>Dobbertin</math></td> | ||
<td>Dobbertin</td> | |||
<td>280604</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 221: | Line 320: | ||
<td><math>x^6+x^{33}+p^{31}x^{192}</math></td> | <td><math>x^6+x^{33}+p^{31}x^{192}</math></td> | ||
<td><math>C3</math></td> | <td><math>C3</math></td> | ||
<td>Gold</td> | |||
<td>151216</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 227: | Line 329: | ||
<td><math>x^{33}+x^{72}+p^{31}x^{258}</math></td> | <td><math>x^{33}+x^{72}+p^{31}x^{258}</math></td> | ||
<td><math>C3</math></td> | <td><math>C3</math></td> | ||
<td>Gold</td> | |||
<td>153896</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 233: | Line 338: | ||
<td><math>x^3+Tr_{10}(x^9)</math></td> | <td><math>x^3+Tr_{10}(x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td>164034</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 239: | Line 347: | ||
<td><math>x^3+a^{-1}Tr_{10}(a^3x^9)</math></td> | <td><math>x^3+a^{-1}Tr_{10}(a^3x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td>164098</td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 246: | Line 357: | ||
<td><math>x^3</math></td> | <td><math>x^3</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 252: | Line 366: | ||
<td><math>x^5</math></td> | <td><math>x^5</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 258: | Line 375: | ||
<td><math>x^9</math></td> | <td><math>x^9</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 264: | Line 384: | ||
<td><math>x^{17}</math></td> | <td><math>x^{17}</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 270: | Line 393: | ||
<td><math>x^{33}</math></td> | <td><math>x^{33}</math></td> | ||
<td><math>Gold</math></td> | <td><math>Gold</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 276: | Line 402: | ||
<td><math>x^{13}</math></td> | <td><math>x^{13}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 282: | Line 411: | ||
<td><math>x^{57}</math></td> | <td><math>x^{57}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 287: | Line 419: | ||
<td><math>x^{241}</math></td> | <td><math>x^{241}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 292: | Line 427: | ||
<td><math>x^{993}</math></td> | <td><math>x^{993}</math></td> | ||
<td><math>Kasami</math></td> | <td><math>Kasami</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 297: | Line 435: | ||
<td><math>x^{35}</math></td> | <td><math>x^{35}</math></td> | ||
<td><math>Welch</math></td> | <td><math>Welch</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 302: | Line 443: | ||
<td><math>x^{287}</math></td> | <td><math>x^{287}</math></td> | ||
<td><math>Niho</math></td> | <td><math>Niho</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 307: | Line 451: | ||
<td><math>x^{123}</math></td> | <td><math>x^{123}</math></td> | ||
<td><math>Inverse</math></td> | <td><math>Inverse</math></td> | ||
<td>Inverse</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
Line 312: | Line 459: | ||
<td><math>x^3+Tr_{11}(x^9)</math></td> | <td><math>x^3+Tr_{11}(x^9)</math></td> | ||
<td><math>C4</math></td> | <td><math>C4</math></td> | ||
<td>Gold</td> | |||
<td></td> | |||
<td></td> | |||
</tr> | </tr> | ||
</table> | </table> |
Revision as of 10:36, 26 July 2019
CCZ-inequivalent APN Functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] from the Known APN Classes for [math]\displaystyle{ 6\leqslant n \leqslant 11 }[/math]
Dimension | [math]\displaystyle{ N^\circ }[/math] | Functions | Equivalent to | Walsh spectrum | Γ-rank | Δ-rank |
---|---|---|---|---|---|---|
[math]\displaystyle{ 6 }[/math] | [math]\displaystyle{ 6.1 }[/math] | [math]\displaystyle{ x^3 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 1102 | 94 |
[math]\displaystyle{ 6.2 }[/math] | [math]\displaystyle{ x^{24}+ax^{17}+a^8x^{10}+ax^9+x^3 }[/math] | [math]\displaystyle{ C3 }[/math] | Gold | 1146 | 94 | |
[math]\displaystyle{ 6.3 }[/math] | [math]\displaystyle{ ax^3+x^{17}+a^4x^{24} }[/math] | [math]\displaystyle{ C7-C9 }[/math] | Gold | 1166 | 96 | |
[math]\displaystyle{ 7 }[/math] | [math]\displaystyle{ 7.1 }[/math] | [math]\displaystyle{ x^3 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 3610 | 198 |
[math]\displaystyle{ 7.2 }[/math] | [math]\displaystyle{ x^5 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 3708 | 198 | |
[math]\displaystyle{ 7.3 }[/math] | [math]\displaystyle{ x^9 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 3610 | 198 | |
[math]\displaystyle{ 7.4 }[/math] | [math]\displaystyle{ x^{13} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | 4270 | 338 | |
[math]\displaystyle{ 7.5 }[/math] | [math]\displaystyle{ x^{57} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | 4704 | 436 | |
[math]\displaystyle{ 7.6 }[/math] | [math]\displaystyle{ x^{63} }[/math] | [math]\displaystyle{ Inverse }[/math] | Inverse | 8128 | 4928 | |
[math]\displaystyle{ 7.7 }[/math] | [math]\displaystyle{ x^3+Tr_7(x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold | 4026 | 212 | |
[math]\displaystyle{ 8 }[/math] | [math]\displaystyle{ 8.1 }[/math] | [math]\displaystyle{ x^3 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 11818 | 420 |
[math]\displaystyle{ 8.2 }[/math] | [math]\displaystyle{ x^9 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 12370 | 420 | |
[math]\displaystyle{ 8.3 }[/math] | [math]\displaystyle{ x^{57} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | 15358 | 960 | |
[math]\displaystyle{ 8.4 }[/math] | [math]\displaystyle{ x^3+x^{17}+p^{48}x^{18}+p^3x^{33}+px^{34}+x^{48} }[/math] | [math]\displaystyle{ C3 }[/math] | Gold | 13200 | 414 | |
[math]\displaystyle{ 8.5 }[/math] | [math]\displaystyle{ x^3+Tr_8(x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold | 13200 | 432 | |
[math]\displaystyle{ 8.6 }[/math] | [math]\displaystyle{ x^3+a^{-1}Tr_8(a^3x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold | 13842 | 436 | |
[math]\displaystyle{ 8.7 }[/math] | [math]\displaystyle{ a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12} }[/math] | [math]\displaystyle{ C10 }[/math] | Gold | 13642 | 436 | |
[math]\displaystyle{ 9 }[/math] | [math]\displaystyle{ 9.1 }[/math] | [math]\displaystyle{ x^3 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 38470 | 872 |
[math]\displaystyle{ 9.2 }[/math] | [math]\displaystyle{ x^5 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 41494 | 872 | |
[math]\displaystyle{ 9.3 }[/math] | [math]\displaystyle{ x^{17} }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 38470 | 872 | |
[math]\displaystyle{ 9.4 }[/math] | [math]\displaystyle{ x^{13} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | 58676 | 3086 | |
[math]\displaystyle{ 9.5 }[/math] | [math]\displaystyle{ x^{241} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | 61726 | 3482 | |
[math]\displaystyle{ 9.6 }[/math] | [math]\displaystyle{ x^{19} }[/math] | [math]\displaystyle{ Welch }[/math] | Gold | 60894 | 3956 | |
[math]\displaystyle{ 9.7 }[/math] | [math]\displaystyle{ x^{255} }[/math] | [math]\displaystyle{ Inverse }[/math] | Inverse | 130816 | 93024 | |
[math]\displaystyle{ 9.8 }[/math] | [math]\displaystyle{ x^3+Tr_9(x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold | 47890 | 920 | |
[math]\displaystyle{ 9.9 }[/math] | [math]\displaystyle{ x^3+Tr^3_9(x^9+x^{18}) }[/math] | [math]\displaystyle{ C5 }[/math] | Gold | 48428 | 930 | |
[math]\displaystyle{ 9.10 }[/math] | [math]\displaystyle{ x^3+Tr^3_9(x^{18}+x^{36}) }[/math] | [math]\displaystyle{ C6 }[/math] | Gold | 48460 | 944 | |
[math]\displaystyle{ 9.11 }[/math] | [math]\displaystyle{ x^3+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129} }[/math] | [math]\displaystyle{ C11 }[/math] | Gold | 48596 | 944 | |
[math]\displaystyle{ 10 }[/math] | [math]\displaystyle{ 10.1 }[/math] | [math]\displaystyle{ x^3 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 125042 | |
[math]\displaystyle{ 10.2 }[/math] | [math]\displaystyle{ x^9 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | 136492 | ||
[math]\displaystyle{ 10.3 }[/math] | [math]\displaystyle{ x^{57} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | 186416 | ||
[math]\displaystyle{ 10.4 }[/math] | [math]\displaystyle{ x^{339} }[/math] | [math]\displaystyle{ Dobbertin }[/math] | Dobbertin | 280604 | ||
[math]\displaystyle{ 10.5 }[/math] | [math]\displaystyle{ x^6+x^{33}+p^{31}x^{192} }[/math] | [math]\displaystyle{ C3 }[/math] | Gold | 151216 | ||
[math]\displaystyle{ 10.6 }[/math] | [math]\displaystyle{ x^{33}+x^{72}+p^{31}x^{258} }[/math] | [math]\displaystyle{ C3 }[/math] | Gold | 153896 | ||
[math]\displaystyle{ 10.7 }[/math] | [math]\displaystyle{ x^3+Tr_{10}(x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold | 164034 | ||
[math]\displaystyle{ 10.8 }[/math] | [math]\displaystyle{ x^3+a^{-1}Tr_{10}(a^3x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold | 164098 | ||
[math]\displaystyle{ 11 }[/math] | [math]\displaystyle{ 11.1 }[/math] | [math]\displaystyle{ x^3 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | ||
[math]\displaystyle{ 11.2 }[/math] | [math]\displaystyle{ x^5 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | |||
[math]\displaystyle{ 11.3 }[/math] | [math]\displaystyle{ x^9 }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | |||
[math]\displaystyle{ 11.4 }[/math] | [math]\displaystyle{ x^{17} }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | |||
[math]\displaystyle{ 11.5 }[/math] | [math]\displaystyle{ x^{33} }[/math] | [math]\displaystyle{ Gold }[/math] | Gold | |||
[math]\displaystyle{ 11.6 }[/math] | [math]\displaystyle{ x^{13} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | |||
[math]\displaystyle{ 11.7 }[/math] | [math]\displaystyle{ x^{57} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | |||
[math]\displaystyle{ 11.8 }[/math] | [math]\displaystyle{ x^{241} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | |||
[math]\displaystyle{ 11.9 }[/math] | [math]\displaystyle{ x^{993} }[/math] | [math]\displaystyle{ Kasami }[/math] | Gold | |||
[math]\displaystyle{ 11.10 }[/math] | [math]\displaystyle{ x^{35} }[/math] | [math]\displaystyle{ Welch }[/math] | Gold | |||
[math]\displaystyle{ 11.11 }[/math] | [math]\displaystyle{ x^{287} }[/math] | [math]\displaystyle{ Niho }[/math] | Gold | |||
[math]\displaystyle{ 11.12 }[/math] | [math]\displaystyle{ x^{123} }[/math] | [math]\displaystyle{ Inverse }[/math] | Inverse | |||
[math]\displaystyle{ 11.13 }[/math] | [math]\displaystyle{ x^3+Tr_{11}(x^9) }[/math] | [math]\displaystyle{ C4 }[/math] | Gold |