Difference between revisions of "Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8"

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Line 8: Line 8:
 
<th><math>N^\circ</math></th>
 
<th><math>N^\circ</math></th>
 
<th><math>F(x)</math></th>
 
<th><math>F(x)</math></th>
 +
<th>Γ-rank</th>
 +
<th>Δ-rank</th>
 +
<th>Aut(dev(G<sub>F</sub>))/2<sup>2n</sup></th>
 +
<th>Aut(dev(G<sub>F</sub>))/2<sup>2n</sup></th>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 13: Line 17:
 
<td>1.1</td>
 
<td>1.1</td>
 
<td><math>x^3</math></td>
 
<td><math>x^3</math></td>
 +
<td>330</td>
 +
<td>42</td>
 +
<td>4960</td>
 +
<td>4960</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>1.2</td>
 
<td>1.2</td>
 
<td><math>x^5</math></td>
 
<td><math>x^5</math></td>
 +
<td>330</td>
 +
<td>42</td>
 +
<td>4960</td>
 +
<td>158720</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.1</td>
 
<td>2.1</td>
 
<td><math>x^{-1}</math></td>
 
<td><math>x^{-1}</math></td>
 +
<td>496</td>
 +
<td>232</td>
 +
<td>310</td>
 +
<td>310</td>
 
</tr>
 
</tr>
 
</tr>
 
</tr>
Line 27: Line 43:
 
<td>1.1</td>
 
<td>1.1</td>
 
<td><math>x^{3}</math></td>
 
<td><math>x^{3}</math></td>
 +
<td>1102</td>
 +
<td>94</td>
 +
<td>24192</td>
 +
<td>48384</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>1.2</td>
 
<td>1.2</td>
 
<td><math>x^{3} + u^{11}x^{6} + ux^{9}</math></td>
 
<td><math>x^{3} + u^{11}x^{6} + ux^{9}</math></td>
 +
<td>1146</td>
 +
<td>94</td>
 +
<td>4032</td>
 +
<td>8064</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.1</td>
 
<td>2.1</td>
 
<td><math>ux^{5} + x^{9} + u^{4}x^{17} + ux^{18} + u^{4}x^{20} + ux^{24} + u^{4}x^{34} + ux^{40}</math></td>
 
<td><math>ux^{5} + x^{9} + u^{4}x^{17} + ux^{18} + u^{4}x^{20} + ux^{24} + u^{4}x^{34} + ux^{40}</math></td>
 +
<td>1158</td>
 +
<td>96</td>
 +
<td>320</td>
 +
<td>320</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.2</td>
 
<td>2.2</td>
 
<td><math>u^{7}x^{3} + x^{5} + u^{3}x^{9} + u^{4}x^{10} + x^{17} + u^{6}x^{18}</math></td>
 
<td><math>u^{7}x^{3} + x^{5} + u^{3}x^{9} + u^{4}x^{10} + x^{17} + u^{6}x^{18}</math></td>
 +
<td>1166</td>
 +
<td>94</td>
 +
<td>448</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.3</td>
 
<td>2.3</td>
 
<td><math>x^{3} + ux^{24} + x^{10}</math></td>
 
<td><math>x^{3} + ux^{24} + x^{10}</math></td>
 +
<td>1166</td>
 +
<td>96</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.4</td>
 
<td>2.4</td>
 
<td><math>x^{3} + u^{17}(x^{17} + x^{18} + x^{20} + x^{24})</math></td>
 
<td><math>x^{3} + u^{17}(x^{17} + x^{18} + x^{20} + x^{24})</math></td>
 +
<td>1168</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.5</td>
 
<td>2.5</td>
 
<td><math>x^{3} + u^{11}x^{5} + u^{13}x^{9} + x^{17} + u^{11}x^{33} + x^{48}</math></td>
 
<td><math>x^{3} + u^{11}x^{5} + u^{13}x^{9} + x^{17} + u^{11}x^{33} + x^{48}</math></td>
 +
<td>1170</td>
 +
<td>96</td>
 +
<td>320</td>
 +
<td>320</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.6</td>
 
<td>2.6</td>
 
<td><math>u^{25}x^{5} + x^{9} + u^{38}x^{12} + u^{25}x^{18} + u^{25}x^{36}</math></td>
 
<td><math>u^{25}x^{5} + x^{9} + u^{38}x^{12} + u^{25}x^{18} + u^{25}x^{36}</math></td>
 +
<td>1170</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.7</td>
 
<td>2.7</td>
 
<td><math>u^{40}x^{5} + u^{10}x^{6} + u^{62}x^{20} + u^{35}x^{33} + u^{15}x^{34} + u^{29}x^{48}</math></td>
 
<td><math>u^{40}x^{5} + u^{10}x^{6} + u^{62}x^{20} + u^{35}x^{33} + u^{15}x^{34} + u^{29}x^{48}</math></td>
 +
<td>1170</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.8</td>
 
<td>2.8</td>
 
<td><math>u^{34}x^{6} + u^{52}x^{9} + u^{48}x^{12} + u^{6}x^{20} + u^{9}x^{33} + u^{23}x^{34} + u^{25}x^{40}</math></td>
 
<td><math>u^{34}x^{6} + u^{52}x^{9} + u^{48}x^{12} + u^{6}x^{20} + u^{9}x^{33} + u^{23}x^{34} + u^{25}x^{40}</math></td>
 +
<td>1170</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.9</td>
 
<td>2.9</td>
 
<td><math>x^{9} + u^{4}(x^{10} + x^{18}) + u^{9}(x^{12} + x^{20} + x^{40})</math></td>
 
<td><math>x^{9} + u^{4}(x^{10} + x^{18}) + u^{9}(x^{12} + x^{20} + x^{40})</math></td>
 +
<td>1172</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.10</td>
 
<td>2.10</td>
 
<td><math>u^{52}x^{3} + u^{47}x^{5} + ux^{6} + u^{9}x^{9} + u^{44}x^{12} + u^{47}x^{33} + u^{10}x^{34} + u^{33}x^{40}</math></td>
 
<td><math>u^{52}x^{3} + u^{47}x^{5} + ux^{6} + u^{9}x^{9} + u^{44}x^{12} + u^{47}x^{33} + u^{10}x^{34} + u^{33}x^{40}</math></td>
 +
<td>1172</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.11</td>
 
<td>2.11</td>
 
<td><math>u(x^{6} + x^{10} + x^{24} + x^{33}) + x^{9} + u^{4}x^{17}</math></td>
 
<td><math>u(x^{6} + x^{10} + x^{24} + x^{33}) + x^{9} + u^{4}x^{17}</math></td>
 +
<td>1174</td>
 +
<td>96</td>
 +
<td>64</td>
 +
<td>64</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
 
<td>2.12</td>
 
<td>2.12</td>
 
<td><math>x^{3} + </math> <math>u^{17}(x^{17} + </math> <math>x^{18} + </math> <math>x^{20} + </math> <math>x^{24}) + </math> <math>u^{14}((u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{2} + </math> <math>(u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{4}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{8}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{16}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{32}+ (u^{2}x)^{9} +(u^{2}x)^{19} +(u^{2}x)^{36} + </math> <math>x^{21}+x^{42}</math></td>
 
<td><math>x^{3} + </math> <math>u^{17}(x^{17} + </math> <math>x^{18} + </math> <math>x^{20} + </math> <math>x^{24}) + </math> <math>u^{14}((u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{2} + </math> <math>(u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{4}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{8}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{16}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{32}+ (u^{2}x)^{9} +(u^{2}x)^{19} +(u^{2}x)^{36} + </math> <math>x^{21}+x^{42}</math></td>
 +
<td>1300</td>
 +
<td>152</td>
 +
<td>8</td>
 +
<td>8</td>
 
</tr>
 
</tr>
 
<tr class="strongDivider">
 
<tr class="strongDivider">
Line 86: Line 158:
 
x^{3}
 
x^{3}
 
</math></td>
 
</math></td>
 +
<td>3610</td>
 +
<td>198</td>
 +
<td>113792</td>
 +
<td>113792</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 92: Line 168:
 
x^{3} + {\rm Tr}(x^{9})
 
x^{3} + {\rm Tr}(x^{9})
 
</math></td>
 
</math></td>
 +
<td>4026</td>
 +
<td>212</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 98: Line 178:
 
x^{34} + x^{18} + x^{5}
 
x^{34} + x^{18} + x^{5}
 
</math></td>
 
</math></td>
 +
<td>4034</td>
 +
<td>210</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 104: Line 188:
 
x^{3} + x^{17} + x^{33} + x^{34}
 
x^{3} + x^{17} + x^{33} + x^{34}
 
</math></td>
 
</math></td>
 +
<td>4040</td>
 +
<td>212</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 110: Line 198:
 
x^{5}
 
x^{5}
 
</math></td>
 
</math></td>
 +
<td>3708</td>
 +
<td>198</td>
 +
<td>113792</td>
 +
<td>113792</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 116: Line 208:
 
x^{9}
 
x^{9}
 
</math></td>
 
</math></td>
 +
<td>3610</td>
 +
<td>198</td>
 +
<td>113792</td>
 +
<td>14565376</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 122: Line 218:
 
x^{13}
 
x^{13}
 
</math></td>
 
</math></td>
 +
<td>4270</td>
 +
<td>338</td>
 +
<td>889</td>
 +
<td>889</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 128: Line 228:
 
x^{57}
 
x^{57}
 
</math></td>
 
</math></td>
 +
<td>4704</td>
 +
<td>436</td>
 +
<td>889</td>
 +
<td>889</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 134: Line 238:
 
x^{-1}
 
x^{-1}
 
</math></td>
 
</math></td>
 +
<td>8128</td>
 +
<td>4928</td>
 +
<td>1778</td>
 +
<td>1778</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 140: Line 248:
 
x^{65} + x^{10} + x^{3}
 
x^{65} + x^{10} + x^{3}
 
</math></td>
 
</math></td>
 +
<td>4038</td>
 +
<td>212</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 146: Line 258:
 
x^{3} + x^{9} + x^{18} + x^{66}
 
x^{3} + x^{9} + x^{18} + x^{66}
 
</math></td>
 
</math></td>
 +
<td>4044</td>
 +
<td>212</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 152: Line 268:
 
x^{3} + x^{12} + x^{17} + x^{33}
 
x^{3} + x^{12} + x^{17} + x^{33}
 
</math></td>
 
</math></td>
 +
<td>4048</td>
 +
<td>210</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 158: Line 278:
 
x^{3} + x^{17} + x^{20} + x^{34} + x^{66}
 
x^{3} + x^{17} + x^{20} + x^{34} + x^{66}
 
</math></td>
 
</math></td>
 +
<td>4040</td>
 +
<td>210</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 164: Line 288:
 
x^{3} + x^{20} + x^{34} + x^{66}
 
x^{3} + x^{20} + x^{34} + x^{66}
 
</math></td>
 
</math></td>
 +
<td>4048</td>
 +
<td>210</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 170: Line 298:
 
x^{3} + x^{12} + x^{40} + x^{72}
 
x^{3} + x^{12} + x^{40} + x^{72}
 
</math></td>
 
</math></td>
 +
<td>4048</td>
 +
<td>210</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 176: Line 308:
 
x^{3} + x^{5} + x^{10} + x^{33} + x^{34}
 
x^{3} + x^{5} + x^{10} + x^{33} + x^{34}
 
</math></td>
 
</math></td>
 +
<td>4040</td>
 +
<td>212</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 182: Line 318:
 
x^{3} + x^{6} + x^{34} + x^{40} + x^{72}
 
x^{3} + x^{6} + x^{34} + x^{40} + x^{72}
 
</math></td>
 
</math></td>
 +
<td>4048</td>
 +
<td>212</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 188: Line 328:
 
x^{3} + x^{5} + x^{6} + x^{12} + x^{33} + x^{34}
 
x^{3} + x^{5} + x^{6} + x^{12} + x^{33} + x^{34}
 
</math></td>
 
</math></td>
 +
<td>4050</td>
 +
<td>210</td>
 +
<td>896</td>
 +
<td>896</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 194: Line 338:
 
u^{2}x^{96} + </math> <math>u^{78}x^{80} + </math> <math>u^{121}x^{72} + </math> <math>u^{49}x^{68} + </math> <math>u^{77}x^{66} + </math> <math>u^{29}x^{65} + </math> <math>u^{119}x^{48} + </math> <math>u^{117}x^{40} + </math> <math>u^{28}x^{36} + </math> <math>u^{107}x^{34} +u^{62}x^{33} +u^{125}x^{24} +u^{76}x^{20} +u^{84}x^{18} +u^{110}x^{17} +u^{49}x^{12} +u^{102}x^{10} +u^{69}x^{9} + </math> <math>u^{14}x^{6} + </math> <math>x^{5} + </math> <math>x^{3}
 
u^{2}x^{96} + </math> <math>u^{78}x^{80} + </math> <math>u^{121}x^{72} + </math> <math>u^{49}x^{68} + </math> <math>u^{77}x^{66} + </math> <math>u^{29}x^{65} + </math> <math>u^{119}x^{48} + </math> <math>u^{117}x^{40} + </math> <math>u^{28}x^{36} + </math> <math>u^{107}x^{34} +u^{62}x^{33} +u^{125}x^{24} +u^{76}x^{20} +u^{84}x^{18} +u^{110}x^{17} +u^{49}x^{12} +u^{102}x^{10} +u^{69}x^{9} + </math> <math>u^{14}x^{6} + </math> <math>x^{5} + </math> <math>x^{3}
 
</math></td>
 
</math></td>
 +
<td>4046</td>
 +
<td>212</td>
 +
<td>128</td>
 +
<td>128</td>
 
</tr>
 
</tr>
 
<tr class="strongDivider">
 
<tr class="strongDivider">
Line 201: Line 349:
 
x^{3}
 
x^{3}
 
</math></td>
 
</math></td>
 +
<td>11818</td>
 +
<td>420</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 207: Line 359:
 
x^{9}
 
x^{9}
 
</math></td>
 
</math></td>
 +
<td>12370</td>
 +
<td>420</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 213: Line 369:
 
x^{3}+{\rm Tr}(x^{9})
 
x^{3}+{\rm Tr}(x^{9})
 
</math></td>
 
</math></td>
 +
<td>13800</td>
 +
<td>432</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 219: Line 379:
 
x^{9}+{\rm Tr}(x^{3})
 
x^{9}+{\rm Tr}(x^{3})
 
</math></td>
 
</math></td>
 +
<td>13804</td>
 +
<td>434</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 225: Line 389:
 
x^{3}+u^{245}x^{33}+u^{183}x^{66}+u^{21}x^{144}
 
x^{3}+u^{245}x^{33}+u^{183}x^{66}+u^{21}x^{144}
 
</math></td>
 
</math></td>
 +
<td>13842</td>
 +
<td>436</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 231: Line 399:
 
x^{3} + u^{65}x^{18}+u^{120}x^{66}+u^{135}x^{144}
 
x^{3} + u^{65}x^{18}+u^{120}x^{66}+u^{135}x^{144}
 
</math></td>
 
</math></td>
 +
<td>13848</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 237: Line 409:
 
u^{188}x^{192} + </math> <math>u^{129}x^{144} + </math> <math>u^{172}x^{132} + </math> <math> u^{138}x^{129} + </math> <math>u^{74}x^{96} + </math> <math>u^{244}x^{72} + </math> <math>u^{22}x^{66} + </math> <math> u^{178}x^{48} + </math> <math>u^{150}x^{36} + </math> <math>u^{146}x^{33} + </math> <math>u^{6}x^{24} + </math> <math> u^{60}x^{18} + </math> <math>u^{80}x^{12} + </math> <math>u^{140}x^{9} + </math> <math>u^{221}x^{6} + </math> <math>u^{19}x^{3}
 
u^{188}x^{192} + </math> <math>u^{129}x^{144} + </math> <math>u^{172}x^{132} + </math> <math> u^{138}x^{129} + </math> <math>u^{74}x^{96} + </math> <math>u^{244}x^{72} + </math> <math>u^{22}x^{66} + </math> <math> u^{178}x^{48} + </math> <math>u^{150}x^{36} + </math> <math>u^{146}x^{33} + </math> <math>u^{6}x^{24} + </math> <math> u^{60}x^{18} + </math> <math>u^{80}x^{12} + </math> <math>u^{140}x^{9} + </math> <math>u^{221}x^{6} + </math> <math>u^{19}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14034</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 243: Line 419:
 
u^{37}x^{192} + </math> <math>u^{110}x^{144} + </math> <math>u^{40}x^{132} + </math> <math>u^{53}x^{129}  + </math> <math>u^{239}x^{96} + </math> <math>u^{235}x^{72} + </math> <math>u^{126}x^{66} + </math> <math>u^{215}x^{48} + </math> <math> u^{96}x^{36} + </math> <math>u^{29}x^{33} + </math> <math>u^{19}x^{24} + </math> <math>u^{14}x^{18} + </math> <math> u^{139}x^{12} + </math> <math>u^{230}x^{9} + </math> <math>u^{234}x^{6} + </math> <math>u^{228}x^{3}
 
u^{37}x^{192} + </math> <math>u^{110}x^{144} + </math> <math>u^{40}x^{132} + </math> <math>u^{53}x^{129}  + </math> <math>u^{239}x^{96} + </math> <math>u^{235}x^{72} + </math> <math>u^{126}x^{66} + </math> <math>u^{215}x^{48} + </math> <math> u^{96}x^{36} + </math> <math>u^{29}x^{33} + </math> <math>u^{19}x^{24} + </math> <math>u^{14}x^{18} + </math> <math> u^{139}x^{12} + </math> <math>u^{230}x^{9} + </math> <math>u^{234}x^{6} + </math> <math>u^{228}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14032</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 249: Line 429:
 
u^{242}x^{192} + </math> <math>u^{100}x^{144} + </math> <math>u^{66}x^{132} + </math> <math>u^{230}x^{129} + </math> <math> u^{202}x^{96} + </math> <math>u^{156}x^{72} + </math> <math>u^{254}x^{66} + </math> <math>u^{18}x^{48} + </math> <math> u^{44}x^{36} + </math> <math>u^{95}x^{33} + </math> <math>u^{100}x^{24} + </math> <math>u^{245}x^{18} + </math> <math> u^{174}x^{12} + </math> <math>u^{175}x^{9} + </math> <math>u^{247}x^{6} + </math> <math>u^{166}x^{3}
 
u^{242}x^{192} + </math> <math>u^{100}x^{144} + </math> <math>u^{66}x^{132} + </math> <math>u^{230}x^{129} + </math> <math> u^{202}x^{96} + </math> <math>u^{156}x^{72} + </math> <math>u^{254}x^{66} + </math> <math>u^{18}x^{48} + </math> <math> u^{44}x^{36} + </math> <math>u^{95}x^{33} + </math> <math>u^{100}x^{24} + </math> <math>u^{245}x^{18} + </math> <math> u^{174}x^{12} + </math> <math>u^{175}x^{9} + </math> <math>u^{247}x^{6} + </math> <math>u^{166}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14036</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 256: Line 440:
 
u^{46}x^{66}+ u^{55}x^{48}+ u^{224}x^{36}+ u^{180}x^{33}+ u^{179}x^{24}+u^{226}x^{18}+ u^{54}x^{12}+ u^{168}x^{9}+ u^{89}x^{6}+ u^{56}x^{3}
 
u^{46}x^{66}+ u^{55}x^{48}+ u^{224}x^{36}+ u^{180}x^{33}+ u^{179}x^{24}+u^{226}x^{18}+ u^{54}x^{12}+ u^{168}x^{9}+ u^{89}x^{6}+ u^{56}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14036</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 262: Line 450:
 
u^{77}x^{192} + </math> <math> u^{133}x^{144} + </math> <math> u^{47}x^{132} + </math> <math> u^{229}x^{129} + </math> <math> u^{23}x^{96} + </math> <math> u^{242}x^{72} + </math> <math> u^{242}x^{66} + </math> <math> u^{245}x^{48} + </math> <math> u^{212}x^{36} + </math> <math> u^{231}x^{33} + </math> <math> u^{174}x^{24} + </math> <math> u^{216}x^{18} + </math> <math> u^{96}x^{12} + </math> <math> u^{253}x^{9} + </math> <math> u^{154}x^{6} + </math> <math> u^{71}x^{3}
 
u^{77}x^{192} + </math> <math> u^{133}x^{144} + </math> <math> u^{47}x^{132} + </math> <math> u^{229}x^{129} + </math> <math> u^{23}x^{96} + </math> <math> u^{242}x^{72} + </math> <math> u^{242}x^{66} + </math> <math> u^{245}x^{48} + </math> <math> u^{212}x^{36} + </math> <math> u^{231}x^{33} + </math> <math> u^{174}x^{24} + </math> <math> u^{216}x^{18} + </math> <math> u^{96}x^{12} + </math> <math> u^{253}x^{9} + </math> <math> u^{154}x^{6} + </math> <math> u^{71}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14032</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 268: Line 460:
 
u^{220}x^{192} + </math> <math> u^{94}x^{144} + </math> <math> u^{70}x^{132} + </math> <math> u^{159}x^{129} + </math> <math> u^{145}x^{96} + </math> <math>u^{160}x^{72} + </math> <math> u^{74}x^{66} + </math> <math> u^{184}x^{48} + </math> <math> u^{119}x^{36} + </math> <math> u^{106}x^{33} + </math> <math>u^{253}x^{24} + </math> <math> wx^{18} + </math> <math> u^{90}x^{12} + </math> <math> u^{169}x^{9} + </math> <math> u^{118}x^{6} + </math> <math> u^{187}x^{3}
 
u^{220}x^{192} + </math> <math> u^{94}x^{144} + </math> <math> u^{70}x^{132} + </math> <math> u^{159}x^{129} + </math> <math> u^{145}x^{96} + </math> <math>u^{160}x^{72} + </math> <math> u^{74}x^{66} + </math> <math> u^{184}x^{48} + </math> <math> u^{119}x^{36} + </math> <math> u^{106}x^{33} + </math> <math>u^{253}x^{24} + </math> <math> wx^{18} + </math> <math> u^{90}x^{12} + </math> <math> u^{169}x^{9} + </math> <math> u^{118}x^{6} + </math> <math> u^{187}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14034</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 274: Line 470:
 
u^{98}x^{192} + </math> <math> u^{225}x^{144} + </math> <math> u^{111}x^{132} + </math> <math> u^{238}x^{129} + </math> <math> u^{182}x^{96} + </math> <math> u^{125}x^{72} + </math> <math> u^{196}x^{66} + </math> <math> u^{219}x^{48} + </math> <math> u^{189}x^{36} + </math> <math> u^{199}x^{33} + </math> <math> u^{181}x^{24} + </math> <math> u^{110}x^{18} + </math> <math> u^{19}x^{12} + </math> <math> u^{175}x^{9} + </math> <math> u^{133}x^{6} + </math> <math> u^{47}x^{3}
 
u^{98}x^{192} + </math> <math> u^{225}x^{144} + </math> <math> u^{111}x^{132} + </math> <math> u^{238}x^{129} + </math> <math> u^{182}x^{96} + </math> <math> u^{125}x^{72} + </math> <math> u^{196}x^{66} + </math> <math> u^{219}x^{48} + </math> <math> u^{189}x^{36} + </math> <math> u^{199}x^{33} + </math> <math> u^{181}x^{24} + </math> <math> u^{110}x^{18} + </math> <math> u^{19}x^{12} + </math> <math> u^{175}x^{9} + </math> <math> u^{133}x^{6} + </math> <math> u^{47}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14030</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 280: Line 480:
 
u^{236}x^{192} + </math> <math> u^{212}x^{160} + </math> <math> u^{153}x^{144} + </math> <math> u^{185}x^{136} + </math> <math> u^{3}x^{132} + </math> <math>u^{89}x^{130} + </math> <math> u^{189}x^{129} + </math> <math> u^{182}x^{96} + </math> <math> u^{105}x^{80} + </math> <math> u^{232}x^{72} + </math> <math>u^{219}x^{68} + </math> <math> u^{145}x^{66} + </math> <math> u^{171}x^{65} + </math> <math> u^{107}x^{48} + </math> <math> u^{179}x^{40} + </math> <math> u^{227}x^{36} + </math> <math> u^{236}x^{34} + </math> <math> u^{189}x^{33} + </math> <math> u^{162}x^{24} + </math> <math> u^{216}x^{20} + </math> <math>u^{162}x^{18} + </math> <math> u^{117}x^{17} + </math> <math> u^{56}x^{12} + </math> <math> u^{107}x^{10} + </math> <math> u^{236}x^{9} + </math> <math>u^{253}x^{6} + </math> <math> u^{180}x^{5} + </math> <math> u^{18}x^{3}
 
u^{236}x^{192} + </math> <math> u^{212}x^{160} + </math> <math> u^{153}x^{144} + </math> <math> u^{185}x^{136} + </math> <math> u^{3}x^{132} + </math> <math>u^{89}x^{130} + </math> <math> u^{189}x^{129} + </math> <math> u^{182}x^{96} + </math> <math> u^{105}x^{80} + </math> <math> u^{232}x^{72} + </math> <math>u^{219}x^{68} + </math> <math> u^{145}x^{66} + </math> <math> u^{171}x^{65} + </math> <math> u^{107}x^{48} + </math> <math> u^{179}x^{40} + </math> <math> u^{227}x^{36} + </math> <math> u^{236}x^{34} + </math> <math> u^{189}x^{33} + </math> <math> u^{162}x^{24} + </math> <math> u^{216}x^{20} + </math> <math>u^{162}x^{18} + </math> <math> u^{117}x^{17} + </math> <math> u^{56}x^{12} + </math> <math> u^{107}x^{10} + </math> <math> u^{236}x^{9} + </math> <math>u^{253}x^{6} + </math> <math> u^{180}x^{5} + </math> <math> u^{18}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14046</td>
 +
<td>454</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 286: Line 490:
 
u^{27}x^{192} + </math> <math> u^{167}x^{144} + </math> <math> u^{26}x^{132} + </math> <math>u^{231}x^{129} + </math> <math> u^{139}x^{96} + </math> <math>u^{30}x^{72} + </math> <math> u^{139}x^{66} + </math> <math> u^{203}x^{48} + </math> <math> u^{36}x^{36} + </math> <math> u^{210}x^{33} + </math> <math>u^{195}x^{24} + </math> <math> u^{12}x^{18} + </math> <math> u^{43}x^{12} + </math> <math> u^{97}x^{9} + </math> <math> u^{61}x^{6} + </math> <math>u^{39}x^{3}
 
u^{27}x^{192} + </math> <math> u^{167}x^{144} + </math> <math> u^{26}x^{132} + </math> <math>u^{231}x^{129} + </math> <math> u^{139}x^{96} + </math> <math>u^{30}x^{72} + </math> <math> u^{139}x^{66} + </math> <math> u^{203}x^{48} + </math> <math> u^{36}x^{36} + </math> <math> u^{210}x^{33} + </math> <math>u^{195}x^{24} + </math> <math> u^{12}x^{18} + </math> <math> u^{43}x^{12} + </math> <math> u^{97}x^{9} + </math> <math> u^{61}x^{6} + </math> <math>u^{39}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14036</td>
 +
<td>454</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 292: Line 500:
 
u^{6}x^{192} + </math> <math> u^{85}x^{144} + </math> <math> u^{251}x^{132} + </math> <math> u^{215}x^{129} + </math> <math> u^{229}x^{96} + </math> <math> u^{195}x^{72} + </math> <math> u^{152}x^{66} + </math> <math> u^{173}x^{48} + </math> <math> u^{209}x^{36} + </math> <math> u^{165}x^{33} + </math> <math> u^{213}x^{24} + </math> <math> u^{214}x^{18} + </math> <math> u^{158}x^{12} + </math> <math> u^{146}x^{9} + </math> <math> x^{6} + </math> <math> u^{50}x^{3}
 
u^{6}x^{192} + </math> <math> u^{85}x^{144} + </math> <math> u^{251}x^{132} + </math> <math> u^{215}x^{129} + </math> <math> u^{229}x^{96} + </math> <math> u^{195}x^{72} + </math> <math> u^{152}x^{66} + </math> <math> u^{173}x^{48} + </math> <math> u^{209}x^{36} + </math> <math> u^{165}x^{33} + </math> <math> u^{213}x^{24} + </math> <math> u^{214}x^{18} + </math> <math> u^{158}x^{12} + </math> <math> u^{146}x^{9} + </math> <math> x^{6} + </math> <math> u^{50}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14032</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 298: Line 510:
 
u^{164}x^{192} + </math> <math> u^{224}x^{144} + </math> <math> u^{59}x^{132} + </math> <math> u^{124}x^{129} + </math> <math> u^{207}x^{96} + </math> <math> u^{211}x^{72} + </math> <math> u^{5}x^{66} + </math> <math> u^{26}x^{48} + </math> <math> u^{20}x^{36} + </math> <math> u^{101}x^{33} + </math> <math> u^{175}x^{24} + </math> <math> u^{241}x^{18} + </math> <math> x^{12} + </math> <math> u^{15}x^{9} + </math> <math> u^{217}x^{6} + </math> <math> u^{212}x^{3}
 
u^{164}x^{192} + </math> <math> u^{224}x^{144} + </math> <math> u^{59}x^{132} + </math> <math> u^{124}x^{129} + </math> <math> u^{207}x^{96} + </math> <math> u^{211}x^{72} + </math> <math> u^{5}x^{66} + </math> <math> u^{26}x^{48} + </math> <math> u^{20}x^{36} + </math> <math> u^{101}x^{33} + </math> <math> u^{175}x^{24} + </math> <math> u^{241}x^{18} + </math> <math> x^{12} + </math> <math> u^{15}x^{9} + </math> <math> u^{217}x^{6} + </math> <math> u^{212}x^{3}
 
</math></td>
 
</math></td>
 +
<td>14028</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 304: Line 520:
 
x^{3}+ x^{17}+u^{16}(x^{18}+x^{33})+u^{15}x^{48}
 
x^{3}+ x^{17}+u^{16}(x^{18}+x^{33})+u^{15}x^{48}
 
</math></td>
 
</math></td>
 +
<td>13200</td>
 +
<td>414</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 310: Line 530:
 
x^{3}+ u^{24}x^{6}+u^{182}x^{132}+u^{67}x^{192}
 
x^{3}+ u^{24}x^{6}+u^{182}x^{132}+u^{67}x^{192}
 
</math></td>
 
</math></td>
 +
<td>14024</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 316: Line 540:
 
x^{3}+x^{6}+x^{68}+x^{80}+x^{132}+x^{160}
 
x^{3}+x^{6}+x^{68}+x^{80}+x^{132}+x^{160}
 
</math></td>
 
</math></td>
 +
<td>14040</td>
 +
<td>454</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 322: Line 550:
 
x^{3}+x^{5}+x^{18}+x^{40}+x^{66}
 
x^{3}+x^{5}+x^{18}+x^{40}+x^{66}
 
</math></td>
 
</math></td>
 +
<td>14044</td>
 +
<td>446</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 328: Line 560:
 
x^{3}+x^{12}+x^{40}+x^{66}+x^{130}
 
x^{3}+x^{12}+x^{40}+x^{66}+x^{130}
 
</math></td>
 
</math></td>
 +
<td>14046</td>
 +
<td>438</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
Line 334: Line 570:
 
x^{57}
 
x^{57}
 
</math></td>
 
</math></td>
 +
<td>15358</td>
 +
<td>960</td>
 +
<td></td>
 +
<td></td>
 
</tr>
 
</tr>
 
</table>
 
</table>

Revision as of 19:44, 8 October 2019

Known switching classes of APN functions over , , and .

Also available is Magma code generating representatives from the switching classes.

Γ-rank Δ-rank Aut(dev(GF))/22n Aut(dev(GF))/22n
1.1 330 42 4960 4960
1.2 330 42 4960 158720
2.1 496 232 310 310
1.1 1102 94 24192 48384
1.2 1146 94 4032 8064
2.1 1158 96 320 320
2.2 1166 94 448 896
2.3 1166 96 896 896
2.4 1168 96 64 64
2.5 1170 96 320 320
2.6 1170 96 64 64
2.7 1170 96 64 64
2.8 1170 96 64 64
2.9 1172 96 64 64
2.10 1172 96 64 64
2.11 1174 96 64 64
2.12 1300 152 8 8
1.1 3610 198 113792 113792
1.2 4026 212 896 896
2.1 4034 210 896 896
2.2 4040 212 896 896
3.1 3708 198 113792 113792
4.1 3610 198 113792 14565376
5.1 4270 338 889 889
6.1 4704 436 889 889
7.1 8128 4928 1778 1778
8.1 4038 212 896 896
9.1 4044 212 896 896
10.1 4048 210 896 896
10.2 4040 210 896 896
11.1 4048 210 896 896
12.1 4048 210 896 896
13.1 4040 212 896 896
14.1 4048 212 896 896
14.2 4050 210 896 896
14.3 4046 212 128 128
1.1 11818 420
1.2 12370 420
1.3 13800 432
1.4 13804 434
1.5 13842 436
1.6 13848 438
1.7 14034 438
1.8 14032 438
1.9 14036 438
1.10 14036 438
1.11 14032 438
1.12 14034 438
1.13 14030 438
1.14 14046 454
1.15 14036 454
1.16 14032 438
1.17 14028 438
2.1 13200 414
3.1 14024 438
4.1 14040 454
5.1 14044 446
6.1 14046 438
7.1 15358 960