Talk:Tables: Difference between revisions

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-== Some APN functions <math>CCZ-</math>equivalent to gold functions and EA-enequivalent to power functions over <math>\mathbb{F}_{2^n}</math> ==
-Some APN functions <math>CCZ-</math>equivalent to gold functions and EA-enequivalent to power functions over <math>\mathbb{F}_{2^n}</math> (constructed in <ref>Budaghyan, Lilya, Claude Carlet, and Alexander Pott. "New classes of almost bent and almost perfect nonlinear polynomials." IEEE Transactions on Information Theory 52.3 (2006): 1141-1152.</ref>
-<table>
-<tr>
-<th>Functions</th>
-<th>Conditions</th>
-<th><math>d^\circ</math></th>
-</tr>
-<tr>
-<td><math>x^{2^i+1}+(x^{2^i}+tr_n(1)+1)tr(x^{2^i+1}+xtr_n(1))</math></td>
-<td><math>n\geq4,\ gcd(i,n)=1</math></td>
-<td>3</td>
-</tr>
-<tr>
-<td><math>x+tr_{n/3}(x^{2(2^i+1)}+x^{4(2^i+1)})+tr_n(x)\, tr_{n/3}(x^{2^i+1}+x^{2^{2i}(2^i+1)})^{2^i+1}</math></td>
-<td><math>6|n,\ gcd(i,n)=1</math></td>
-<td>4</td>
-</tr>
-<tr>
-<td><math>x^{2^i+1}+tr_{n/m}(x^{2^i+1})+x^{2^i}tr_{n/m}(x)+xtr_{n/m}(x)^{2^i}+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1})
-+tr_{n/m}(x)]^{\frac{1}{2^i+1}}(x^{2^i}+tr_{n/m}(x)^{2^i}+1)+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1})
-+tr_{n/m}(x)]^{\frac{2^i}{2^i+1}}(x+tr_{n/m}(x))</math></td>
-<td><math>m\neq n,\ n\ odd,\ m|n,\ gcd(i,n)=1</math></td>
-<td><math>m+2</math></td>
-</tr>
-</table>

Latest revision as of 19:23, 24 December 2018