Difference between revisions of "Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1"

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<tr class="divider">
 
<tr class="divider">
<td rowspan="5"><math>11</math></td>
+
<td><math>11</math></td>
<td class="noborderbelow"><math>11.1</math></td>
 
<td><math>x^{12} + x^{10} + x^9 + x^5 + x^3</math></td>
 
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>
</tr>
 
 
<td><math>11.2</math></td>
 
<td><math>x^{258} + x^{257} + x^{18} + x^{17} + x^3</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
</tr>
 
 
<td><math>11.3</math></td>
 
<td><math>x^{96} + x^{66} + x^{34} + x^{33} + x^3</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
</tr>
 
 
<td><math>11.4</math></td>
 
<td><math>x^{80} + x^{68} + x^{65} + x^{17} + x^5</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
</tr>
 
 
<td><math>11.5</math></td>
 
<td><math>x^{260} + x^{257} + x^{36} + x^{33} + x^5</math></td>
 
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>
 
<td><math>-</math></td>

Latest revision as of 15:57, 19 August 2019

The following tables list CCZ-inequivalent representatives found by systematically searching for APN functions among all trinomials, quadrinomials, pentanomials and hexanomials with coefficients in over with [1]. The tables also list which equivalence class from [2] the functions belong to. Only polynomials inequivalent to power functions are considered. If the polynomial is equivalent to a family from the table of infinite families, this is also listed.

Trinomials

Dimension Functions Familiy Relation to [2]
Table 7: № 8.1
Table 7: № 2.1
Table 9: № 1.3
Table 9: № 1.4

Quadrinomials

Dimension Functions Families Relation to [2]
Table 7: № 12.1
Table 7: № 2.2
Table 7: № 10.1
Table 7: № 11.1
Table 7: № 8.1
Table 7: № 9.1

Pentanomials

Dimension Functions Families Relation to [2]
Table 7: № 13.1
Table 7: № 1.2
Table 7: № 12.1
Table 7: № 1.2
Table 7: № 11.1
Table 7: № 10.1
Table 7: № 2.1
Table 7: № 14.1
Table 7: № 8.1
Table 7: № 10.1
Table 9: № 1.4
Table 9: № 1.3
Table 9: № 6.1
Table 9: № 5.1

Hexanomials

Dimension Functions Families Relation to [2]
Table 7: № 14.2
Table 7: № 14.1
Table 7: № 12.1
Table 7: № 2.1
Table 7: № 1.2
Table 7: № 11.1
Table 7: № 2.2
Table 7: № 9.1
Table 7: № 13.1
Table 7: № 10.1
Table 7: № 10.2
Table 7: № 8.1
Table 9: № 5.1
Table 9: № 6.1
Table 9: № 4.1
  1. Sun B. On Classification and Some Properties of APN Functions.
  2. 2.0 2.1 2.2 2.3 2.4 Edel Y, Pott A. A new almost perfect nonlinear function which is not quadratic. Adv. in Math. of Comm.. 2009 Mar;3(1):59-81.