View source for CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n between 6 and 11)

CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n is equal or larger than 6 and equal or smaller than 11)

<table>
<tr>
<th><math>N^\circ</math></th>
<th>Functions*</th>
<th><math>n=6</math></th>
<th><math>n=7</math></th>
<th><math>n=8</math></th>
<th><math>n=9</math></th>
<th><math>n=10</math></th>
<th><math>n=11</math></th>
</tr>

<tr>
<td><math>1</math></td>
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math>
<math>p=3</math>
<td>Gold</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
</tr>

<tr>
<td><math>2</math></td>
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math>
<math>p=4</math>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
</tr>

<tr>
<td><math>3</math></td>
<td><math>x^{2^{2i}+2^i}+bx^{q+1}+cx^{q(2^{2i}+2^i)}</math></td>
<td>New</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>New I (<math>i=1, c=u^{31}, b=1)</math>
New II (<math>i=3, c=u^{31}, b=1)</math>
<td>-</td>
</tr>

<tr>
<td><math>4</math></td>
<td><math>x(x^{2^i}+x^q+cx^{2^iq})+x^{2^i}(c^qx^q+sx^{2^iq})+x^{(2^i+1)}q</math></td>
<td><math>N^\circ 3</math></td>
<td>-</td>
<td>New</td>
<td>-</td>
<td><math>N^\circ3</math>: Case I <math>(i=1, c=u^3, s=u)</math>
<math>N^\circ3</math>: Case II <math>(i=3, c=u^3, s=w)</math>
<td>-</td>
</tr>


<tr>
<td><math>5</math></td>
<td><math>x^3+a^{-1}tr_n(a^3x^9)</math></td>
<td>Gold<math>(a=1)</math>
<math>N^\circ 3 (a=u)</math>
<td>New</td>
<td>New I <math>(a=1)</math>
New II <math>(a=u)</math>
<td>New</td>
<td>New I <math>(a=1)</math>
New II <math>(a=u)</math>
<td>New</td>
</tr>


<tr>
<td><math>6</math></td>
<td><math>x^3+a^{-1}tr_n^3(a^3x^9+a^6x^{18})</math></td>
<td>Gold<math>(a=1)</math>
<math>N^\circ 3 (a=u)</math>
<td>-</td>
<td>-</td>
<td>New</td>
<td>-</td>
<td>-</td>
</tr>


<tr>
<td><math>7</math></td>
<td><math>x^3+a^{-1}tr_n^3(a^6x^{18}+a^{12}x^{36})</math></td>
<td>Gold<math>(a=1)</math>
<math>N^\circ 3 (a=u)</math>
<td>-</td>
<td>-</td>
<td>New</td>
<td>-</td>
<td>-</td>
</tr>


<tr>
<td><math>8</math></td>
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
<math>v=0, w\ne0</math>
<td>New</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
</tr>


<tr>
<td><math>9</math></td>
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
<math>v\ne0, w=0</math>
<td><math>N^\circ8</math></td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
</tr>



<tr>
<td><math>10</math></td>
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
<math>v\ne0, w=0</math>
<td><math>N^\circ8</math></td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
</tr>



<tr>
<td><math>11</math></td>
<td><math>(x+x^{2^m})^{2^k+1}+u^{(2^{n}-1)/(2^m-1)}(u x+u^{2^m}x^{2^m})^{(2^k+1)2^i}+u(x+x^{2^m})(u x+u ^{2^m}x^{2^m})</math>
<td><math>-</math></td>
<td>-</td>
<td>New <math>(i=2)</math>
<math>N^\circ4 (i=0)</math>
<td>-</td>
<td>-</td>
<td>-</td>
</tr>

</table>