CCZ-inequivalent representatives from the known APN families for dimensions up to 11: Difference between revisions

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<tr>
<tr>
<th>Dimension</th>
<th>Dimension</th>
<th><math>N^\circ</math></th>
<th><span class="htmlMath">N<sup>○</sup></span></th>
<th>Functions</th>
<th>Functions</th>
<th>Equivalent to</th>
<th>Equivalent to</th>
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<tr class="divider">
<tr class="divider">
<td rowspan="3"><math>6</math></td>
<td rowspan="3"><span class="htmlMath">6</span></td>
<td class="noborderbelow"><math>6.1</math></td>
<td class="noborderbelow"><span class="htmlMath">6.1</span></td>
<td><math>x^3</math></td>
<td><span class="htmlMath">x<sup>3</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>1102</td>
<td>1102</td>
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<tr>
<tr>
<td class="noborderbelow"><math>6.2</math></td>
<td class="noborderbelow"><span class="htmlMath">6.2</span></td>
<td><math>x^{24}+ax^{17}+a^8x^{10}+ax^9+x^3</math></td>
<td><span class="htmlMath">x<sup>24</sup>+ax<sup>17</sup>+a<sup>8</sup>x<sup>10</sup>+ax<sup>9</sup>+x<sup>3</sup></span></td>
<td><math>C3</math></td>
<td><span class="htmlMath">C3</span></td>
<td>Gold</td>
<td>Gold</td>
<td>1146</td>
<td>1146</td>
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<tr>
<tr>
<td class="noborderbelow"><math>6.3</math></td>
<td class="noborderbelow"><span class="htmlMath">6.3</span></td>
<td><math>ax^3+x^{17}+a^4x^{24}</math></td>
<td><span class="htmlMath">ax<sup>3</sup>+x<sup>17</sup>+a<sup>4</sup>x<sup>24</sup></span></td>
<td><math>C7-C9</math></td>
<td><span class="htmlMath">C7-C9</span></td>
<td>Gold</td>
<td>Gold</td>
<td>1166</td>
<td>1166</td>
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<tr class="divider">
<tr class="divider">
<td rowspan="7"><math>7</math></td>
<td rowspan="7"><span class="htmlMath">7</span></td>
<td class="noborderbelow"><math>7.1</math></td>
<td class="noborderbelow"><span class="htmlMath">7.1</span></td>
<td><math>x^3</math></td>
<td><span class="htmlMath">x<sup>3</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>3610</td>
<td>3610</td>
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<tr>
<tr>
<td class="noborderbelow"><math>7.2</math></td>
<td class="noborderbelow"><span class="htmlMath">7.2</span></td>
<td><math>x^5</math></td>
<td><span class="htmlMath">x<sup>5</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>3708</td>
<td>3708</td>
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<tr>
<tr>
<td class="noborderbelow"><math>7.3</math></td>
<td class="noborderbelow"><span class="htmlMath">7.3</span></td>
<td><math>x^9</math></td>
<td><span class="htmlMath">x<sup>9</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>3610</td>
<td>3610</td>
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<tr>
<tr>
<td class="noborderbelow"><math>7.4</math></td>
<td class="noborderbelow"><span class="htmlMath">7.4</span></td>
<td><math>x^{13}</math></td>
<td><span class="htmlMath">x<sup>13</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td>4270</td>
<td>4270</td>
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<tr>
<tr>
<td class="noborderbelow"><math>7.5</math></td>
<td class="noborderbelow"><span class="htmlMath">7.5</span></td>
<td><math>x^{57}</math></td>
<td><span class="htmlMath">x<sup>57</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td>4704</td>
<td>4704</td>
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<tr>
<tr>
<td class="noborderbelow"><math>7.6</math></td>
<td class="noborderbelow"><span class="htmlMath">7.6</span></td>
<td><math>x^{63}</math></td>
<td><span class="htmlMath">x<sup>63</sup></span></td>
<td><math>Inverse</math></td>
<td><span class="htmlMath">Inverse</span></td>
<td>Inverse</td>
<td>Inverse</td>
<td>8128</td>
<td>8128</td>
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<tr>
<tr>
<td class="noborderbelow"><math>7.7</math></td>
<td class="noborderbelow"><span class="htmlMath">7.7</span></td>
<td><math>x^3+Tr_7(x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sub>7</sub>(x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td>4026</td>
<td>4026</td>
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<tr class="divider">
<tr class="divider">
<td rowspan="7"><math>8</math></td>
<td rowspan="7"><span class="htmlMath">8</span></td>
<td class="noborderbelow"><math>8.1</math></td>
<td class="noborderbelow"><span class="htmlMath">8.1</span></td>
<td><math>x^3</math></td>
<td><span class="htmlMath">x<sup>3</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>11818</td>
<td>11818</td>
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<tr>
<tr>
<td class="noborderbelow"><math>8.2</math></td>
<td class="noborderbelow"><span class="htmlMath">8.2</span></td>
<td><math>x^9</math></td>
<td><span class="htmlMath">x<sup>9</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>12370</td>
<td>12370</td>
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<tr>
<tr>
<td class="noborderbelow"><math>8.3</math></td>
<td class="noborderbelow"><span class="htmlMath">8.3</span></td>
<td><math>x^{57}</math></td>
<td><span class="htmlMath">x<sup>57</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td>15358</td>
<td>15358</td>
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<tr>
<tr>
<td class="noborderbelow"><math>8.4</math></td>
<td class="noborderbelow"><span class="htmlMath">8.4</span></td>
<td><math>x^3+x^{17}+p^{48}x^{18}+p^3x^{33}+px^{34}+x^{48}</math></td>
<td><span class="htmlMath">x<sup>3</sup>+x<sup>17</sup>+p<sup>48</sup>x<sup>18</sup>+p<sup>3</sup>x<sup>33</sup>+px<sup>34</sup>+x<sup>48</sup></span></td>
<td><math>C3</math></td>
<td><span class="htmlMath">C3</span></td>
<td>Gold</td>
<td>Gold</td>
<td>13200</td>
<td>13200</td>
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<tr>
<tr>
<td class="noborderbelow"><math>8.5</math></td>
<td class="noborderbelow"><span class="htmlMath">8.5</span></td>
<td><math>x^3+Tr_8(x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sub>8</sub>(x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td>13200</td>
<td>13200</td>
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<tr>
<tr>
<td class="noborderbelow"><math>8.6</math></td>
<td class="noborderbelow"><span class="htmlMath">8.6</span></td>
<td><math>x^3+a^{-1}Tr_8(a^3x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+a<sup>-1</sup><span class="latexCommand">Tr</span><sub>8</sub>(a<sup>3</sup>x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td>13842</td>
<td>13842</td>
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<tr>
<tr>
<td class="noborderbelow"><math>8.7</math></td>
<td class="noborderbelow"><span class="htmlMath">8.7</span></td>
<td><math>a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12}</math></td>
<td><span class="htmlMath">a(x+x<sup>16</sup>)(ax+a<sup>16</sup>x<sup>16</sup>)+a<sup>17</sup>(ax+a<sup>16</sup>x<sup>16</sup>)<sup>12</sup></span></td>
<td><math>C10</math></td>
<td><span class="htmlMath">C10</span></td>
<td>Gold</td>
<td>Gold</td>
<td>13642</td>
<td>13642</td>
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<tr class="divider">
<tr class="divider">
<td rowspan="11"><math>9</math></td>
<td rowspan="11"><span class="htmlMath">9</span></td>
<td class="noborderbelow"><math>9.1</math></td>
<td class="noborderbelow"><span class="htmlMath">9.1</span></td>
<td><math>x^3</math></td>
<td><span class="htmlMath">x<sup>3</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>38470</td>
<td>38470</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.2</math></td>
<td class="noborderbelow"><span class="htmlMath">9.2</span></td>
<td><math>x^5</math></td>
<td><span class="htmlMath">x<sup>5</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>41494</td>
<td>41494</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.3</math></td>
<td class="noborderbelow"><span class="htmlMath">9.3</span></td>
<td><math>x^{17}</math></td>
<td><span class="htmlMath">x<sup>17</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>38470</td>
<td>38470</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.4</math></td>
<td class="noborderbelow"><span class="htmlMath">9.4</span></td>
<td><math>x^{13}</math></td>
<td><span class="htmlMath">x<sup>13</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td>58676</td>
<td>58676</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.5</math></td>
<td class="noborderbelow"><span class="htmlMath">9.5</span></td>
<td><math>x^{241}</math></td>
<td><span class="htmlMath">x<sup>241</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td>61726</td>
<td>61726</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.6</math></td>
<td class="noborderbelow"><span class="htmlMath">9.6</span></td>
<td><math>x^{19}</math></td>
<td><span class="htmlMath">x<sup>19</sup></span></td>
<td><math>Welch</math></td>
<td><span class="htmlMath">Welch</span></td>
<td>Gold</td>
<td>Gold</td>
<td>60894</td>
<td>60894</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.7</math></td>
<td class="noborderbelow"><span class="htmlMath">9.7</span></td>
<td><math>x^{255}</math></td>
<td><span class="htmlMath">x<sup>255</sup></span></td>
<td><math>Inverse</math></td>
<td><span class="htmlMath">Inverse</span></td>
<td>Inverse</td>
<td>Inverse</td>
<td>130816</td>
<td>130816</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.8</math></td>
<td class="noborderbelow"><span class="htmlMath">9.8</span></td>
<td><math>x^3+Tr_9(x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sub>9</sub>(x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td>47890</td>
<td>47890</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.9</math></td>
<td class="noborderbelow"><span class="htmlMath">9.9</span></td>
<td><math>x^3+Tr^3_9(x^9+x^{18})</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sup>3</sup><sub>9</sub>(x<sup>9</sup>+x<sup>18</sup>)</span></td>
<td><math>C5</math></td>
<td><span class="htmlMath">C5</span></td>
<td>Gold</td>
<td>Gold</td>
<td>48428</td>
<td>48428</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.10</math></td>
<td class="noborderbelow"><span class="htmlMath">9.10</span></td>
<td><math>x^3+Tr^3_9(x^{18}+x^{36})</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sup>3</sup><sub>9</sub>(x<sup>18</sup>+x<sup>36</sup>)</span></td>
<td><math>C6</math></td>
<td><span class="htmlMath">C6</span></td>
<td>Gold</td>
<td>Gold</td>
<td>48460</td>
<td>48460</td>
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<tr>
<tr>
<td class="noborderbelow"><math>9.11</math></td>
<td class="noborderbelow"><span class="htmlMath">9.11</span></td>
<td><math>x^3+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129}</math></td>
<td><span class="htmlMath">x<sup>3</sup>+a<sup>246</sup>x<sup>10</sup>+a<sup>47</sup>x<sup>17</sup>+a<sup>181</sup>x<sup>66</sup>+a<sup>428</sup>x<sup>129</sup></span></td>
<td><math>C11</math></td>
<td><span class="htmlMath">C11</span></td>
<td>Gold</td>
<td>Gold</td>
<td>48596</td>
<td>48596</td>
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<tr class="divider">
<tr class="divider">
<td rowspan="8"><math>10</math></td>
<td rowspan="10"><span class="htmlMath">10</span></td>
<td class="noborderbelow"><math>10.1</math></td>
<td class="noborderbelow"><span class="htmlMath">10.1</span></td>
<td><math>x^3</math></td>
<td><span class="htmlMath">x<sup>3</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>125042</td>
<td>125042</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.2</math></td>
<td class="noborderbelow"><span class="htmlMath">10.2</span></td>
<td><math>x^9</math></td>
<td><span class="htmlMath">x<sup>9</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td>136492</td>
<td>136492</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.3</math></td>
<td class="noborderbelow"><span class="htmlMath">10.3</span></td>
<td><math>x^{57}</math></td>
<td><span class="htmlMath">x<sup>57</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td>186416</td>
<td>186416</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.4</math></td>
<td class="noborderbelow"><span class="htmlMath">10.4</span></td>
<td><math>x^{339}</math></td>
<td><span class="htmlMath">x<sup>339</sup></span></td>
<td><math>Dobbertin</math></td>
<td><span class="htmlMath">Dobbertin</span></td>
<td>Dobbertin</td>
<td>Dobbertin</td>
<td>280604</td>
<td>280604</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.5</math></td>
<td class="noborderbelow"><span class="htmlMath">10.5</span></td>
<td><math>x^6+x^{33}+p^{31}x^{192}</math></td>
<td><span class="htmlMath">x<sup>6</sup>+x<sup>33</sup>+p<sup>31</sup>x<sup>192</sup></span></td>
<td><math>C3</math></td>
<td><span class="htmlMath">C3</span></td>
<td>Gold</td>
<td>Gold</td>
<td>151216</td>
<td>151216</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.6</math></td>
<td class="noborderbelow"><span class="htmlMath">10.6</span></td>
<td><math>x^{33}+x^{72}+p^{31}x^{258}</math></td>
<td><span class="htmlMath">x<sup>33</sup>+x<sup>72</sup>+p<sup>31</sup>x<sup>258</sup></span></td>
<td><math>C3</math></td>
<td><span class="htmlMath">C3</span></td>
<td>Gold</td>
<td>Gold</td>
<td>153896</td>
<td>153896</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.7</math></td>
<td class="noborderbelow"><span class="htmlMath">10.7</span></td>
<td><math>x^3+Tr_{10}(x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sub>10</sub>(x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td>164034</td>
<td>164034</td>
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<tr>
<tr>
<td class="noborderbelow"><math>10.8</math></td>
<td class="noborderbelow"><span class="htmlMath">10.8</span></td>
<td><math>x^3+a^{-1}Tr_{10}(a^3x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+a<sup>-1</sup><span class="latexCommand">Tr</span><sub>10</sub>(a<sup>3</sup>x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td>164098</td>
<td>164098</td>
<td></td>
</tr>
<tr>
<td class="noborderbelow"><span class="htmlMath">10.9</span></td>
<td><span class="htmlMath">x<sup>3</sup> + p<sup>341</sup>x<sup>9</sup> + p<sup>682</sup>x<sup>96</sup> + x<sup>288</sup></span></td>
<td><span class="htmlMath">C12</span></td>
<td>Gold</td>
<td>166068</td>
<td></td>
</tr>
<tr>
<td class="noborderbelow"><span class="htmlMath">10.10</span></td>
<td><span class="htmlMath">x<sup>3</sup> + p<sup>341</sup>x<sup>129</sup> + p<sup>682</sup>x<sup>96</sup> + x<sup>36</sup></span></td>
<td><span class="htmlMath">C12</span></td>
<td>Gold</td>
<td>166168</td>
<td></td>
<td></td>
</tr>
</tr>


<tr class="divider">
<tr class="divider">
<td rowspan="13"><math>11</math></td>
<td rowspan="13"><span class="htmlMath">11</span></td>
<td class="noborderbelow"><math>11.1</math></td>
<td class="noborderbelow"><span class="htmlMath">11.1</span></td>
<td><math>x^3</math></td>
<td><span class="htmlMath">x<sup>3</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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<tr>
<tr>
<td class="noborderbelow"><math>11.2</math></td>
<td class="noborderbelow"><span class="htmlMath">11.2</span></td>
<td><math>x^5</math></td>
<td><span class="htmlMath">x<sup>5</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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<tr>
<tr>
<td class="noborderbelow"><math>11.3</math></td>
<td class="noborderbelow"><span class="htmlMath">11.3</span></td>
<td><math>x^9</math></td>
<td><span class="htmlMath">x<sup>9</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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<tr>
<tr>
<td class="noborderbelow"><math>11.4</math></td>
<td class="noborderbelow"><span class="htmlMath">11.4</span></td>
<td><math>x^{17}</math></td>
<td><span class="htmlMath">x<sup>17</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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<tr>
<tr>
<td class="noborderbelow"><math>11.5</math></td>
<td class="noborderbelow"><span class="htmlMath">11.5</span></td>
<td><math>x^{33}</math></td>
<td><span class="htmlMath">x<sup>33</sup></span></td>
<td><math>Gold</math></td>
<td><span class="htmlMath">Gold</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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<tr>
<tr>
<td class="noborderbelow"><math>11.6</math></td>
<td class="noborderbelow"><span class="htmlMath">11.6</span></td>
<td><math>x^{13}</math></td>
<td><span class="htmlMath">x<sup>13</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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<tr>
<tr>
<td class="noborderbelow"><math>11.7</math></td>
<td class="noborderbelow"><span class="htmlMath">11.7</span></td>
<td><math>x^{57}</math></td>
<td><span class="htmlMath">x<sup>57</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
Line 416: Line 434:
</tr>
</tr>


<td class="noborderbelow"><math>11.8</math></td>
<td class="noborderbelow"><span class="htmlMath">11.8</span></td>
<td><math>x^{241}</math></td>
<td><span class="htmlMath">x<sup>241</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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</tr>
</tr>


<td class="noborderbelow"><math>11.9</math></td>
<td class="noborderbelow"><span class="htmlMath">11.9</span></td>
<td><math>x^{993}</math></td>
<td><span class="htmlMath">x<sup>993</sup></span></td>
<td><math>Kasami</math></td>
<td><span class="htmlMath">Kasami</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
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</tr>
</tr>


<td class="noborderbelow"><math>11.10</math></td>
<td class="noborderbelow"><span class="htmlMath">11.10</span></td>
<td><math>x^{35}</math></td>
<td><span class="htmlMath">x<sup>35</sup></span></td>
<td><math>Welch</math></td>
<td><span class="htmlMath">Welch</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
Line 440: Line 458:
</tr>
</tr>


<td class="noborderbelow"><math>11.11</math></td>
<td class="noborderbelow"><span class="htmlMath">11.11</span></td>
<td><math>x^{287}</math></td>
<td><span class="htmlMath">x<sup>287</sup></span></td>
<td><math>Niho</math></td>
<td><span class="htmlMath">Niho</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>
Line 448: Line 466:
</tr>
</tr>


<td class="noborderbelow"><math>11.12</math></td>
<td class="noborderbelow"><span class="htmlMath">11.12</span></td>
<td><math>x^{1023}</math></td>
<td><span class="htmlMath">x<sup>1023</sup></span></td>
<td><math>Inverse</math></td>
<td><span class="htmlMath">Inverse</span></td>
<td>Inverse</td>
<td>Inverse</td>
<td></td>
<td></td>
Line 456: Line 474:
</tr>
</tr>


<td class="noborderbelow"><math>11.13</math></td>
<td class="noborderbelow"><span class="htmlMath">11.13</span></td>
<td><math>x^3+Tr_{11}(x^9)</math></td>
<td><span class="htmlMath">x<sup>3</sup>+<span class="latexCommand">Tr</span><sub>11</sub>(x<sup>9</sup>)</span></td>
<td><math>C4</math></td>
<td><span class="htmlMath">C4</span></td>
<td>Gold</td>
<td>Gold</td>
<td></td>
<td></td>

Revision as of 14:07, 11 September 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 N○ Functions Equivalent to Walsh spectrum Γ-rank Δ-rank
6 6.1 x3 Gold Gold 1102 94
6.2 x24+ax17+a8x10+ax9+x3 C3 Gold 1146 94
6.3 ax3+x17+a4x24 C7-C9 Gold 1166 96
7 7.1 x3 Gold Gold 3610 198
7.2 x5 Gold Gold 3708 198
7.3 x9 Gold Gold 3610 198
7.4 x13 Kasami Gold 4270 338
7.5 x57 Kasami Gold 4704 436
7.6 x63 Inverse Inverse 8128 4928
7.7 x3+Tr7(x9) C4 Gold 4026 212
8 8.1 x3 Gold Gold 11818 420
8.2 x9 Gold Gold 12370 420
8.3 x57 Kasami Gold 15358 960
8.4 x3+x17+p48x18+p3x33+px34+x48 C3 Gold 13200 414
8.5 x3+Tr8(x9) C4 Gold 13200 432
8.6 x3+a-1Tr8(a3x9) C4 Gold 13842 436
8.7 a(x+x16)(ax+a16x16)+a17(ax+a16x16)12 C10 Gold 13642 436
9 9.1 x3 Gold Gold 38470 872
9.2 x5 Gold Gold 41494 872
9.3 x17 Gold Gold 38470 872
9.4 x13 Kasami Gold 58676 3086
9.5 x241 Kasami Gold 61726 3482
9.6 x19 Welch Gold 60894 3956
9.7 x255 Inverse Inverse 130816 93024
9.8 x3+Tr9(x9) C4 Gold 47890 920
9.9 x3+Tr39(x9+x18) C5 Gold 48428 930
9.10 x3+Tr39(x18+x36) C6 Gold 48460 944
9.11 x3+a246x10+a47x17+a181x66+a428x129 C11 Gold 48596 944
10 10.1 x3 Gold Gold 125042
10.2 x9 Gold Gold 136492
10.3 x57 Kasami Gold 186416
10.4 x339 Dobbertin Dobbertin 280604
10.5 x6+x33+p31x192 C3 Gold 151216
10.6 x33+x72+p31x258 C3 Gold 153896
10.7 x3+Tr10(x9) C4 Gold 164034
10.8 x3+a-1Tr10(a3x9) C4 Gold 164098
10.9 x3 + p341x9 + p682x96 + x288 C12 Gold 166068
10.10 x3 + p341x129 + p682x96 + x36 C12 Gold 166168
11 11.1 x3 Gold Gold
11.2 x5 Gold Gold
11.3 x9 Gold Gold
11.4 x17 Gold Gold
11.5 x33 Gold Gold
11.6 x13 Kasami Gold
11.7 x57 Kasami Gold
11.8 x241 Kasami Gold
11.9 x993 Kasami Gold
11.10 x35 Welch Gold
11.11 x287 Niho Gold
11.12 x1023 Inverse Inverse
11.13 x3+Tr11(x9) C4 Gold
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