Difference between revisions of "Sigma multiplicities for APN functions in dimensions up to 10"

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(Created page with "For all known APN functions over GF(2^n) with n up to 10, the following tables list the partitions of GF(2^n) induced by the multiplicities of the Sigma sets <math>\Sigma_F^k(...")
 
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<tr><td>9</td><td> 1, 341, 682 </td></tr>
 
<tr><td>9</td><td> 1, 341, 682 </td></tr>
 
<tr><td>10</td><td> 1, 341, 682 </td></tr>
 
<tr><td>10</td><td> 1, 341, 682 </td></tr>
<tr><td>11</td><td> 1, 31, 155, 155, 155, 217, 310 </td></tr>
+
<tr><td>11</td><td> 1, 341, 682 </td></tr>
 
<tr><td>12</td><td> 1, 341, 682 </td></tr>
 
<tr><td>12</td><td> 1, 341, 682 </td></tr>
<tr><td>13</td><td> 1, 124, 217, 310, 372 </td></tr>
+
<tr><td>13</td><td> 1, 341, 682 </td></tr>
 
<tr><td>14</td><td> 1, 341, 682 </td></tr>
 
<tr><td>14</td><td> 1, 341, 682 </td></tr>
<tr><td>15</td><td> 1, 11, 11, 165, 330, 506 </td></tr>
+
<tr><td>15</td><td> 1, 341, 682 </td></tr>
 +
<tr><td>16</td><td> 1, 341, 682 </td></tr>
 +
<tr><td>17</td><td> 1, 31, 155, 155, 155, 217, 310 </td></tr>
 +
<tr><td>18</td><td> 1, 341, 682 </td></tr>
 +
<tr><td>19</td><td> 1, 124, 217, 310, 372 </td></tr>
 +
<tr><td>20</td><td> 1, 341, 682 </td></tr>
 +
<tr><td>21</td><td> 1, 11, 11, 165, 330, 506 </td></tr>
 
</table>
 
</table>

Revision as of 17:40, 2 December 2020

For all known APN functions over GF(2^n) with n up to 10, the following tables list the partitions of GF(2^n) induced by the multiplicities of the Sigma sets <math>\Sigma_F^k(0)</sigma> for k = 4, as explained in the SETA paper on testing EA-equivalences.

Due to the large number of functions, the results for dimension 8 are listed on a separate page.

Dimension 9

Dimension 10

Functions 1-10 are indexed according to [[1]]. The remaining functions correspond to the ones found via self-equivalences, and are indexed in the same way as in the provided dataset.

IDPartition sizes
1 1, 341, 682
2 1, 341, 682
3 1, 341, 682
4 1, 341, 682
5 1, 341, 682
6 1, 341, 682
7 1, 341, 682
8 1, 341, 682
9 1, 341, 682
10 1, 341, 682
11 1, 341, 682
12 1, 341, 682
13 1, 341, 682
14 1, 341, 682
15 1, 341, 682
16 1, 341, 682
17 1, 31, 155, 155, 155, 217, 310
18 1, 341, 682
19 1, 124, 217, 310, 372
20 1, 341, 682
21 1, 11, 11, 165, 330, 506