Two classes of power mappings with boomerang uniformity 2
Two classes of power mappings with boomerang uniformity 2
<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ q $\end{document}</tex-math></inline-formula> be an odd prime power. Let <inline-formula><tex-math id="M2">\begin{document}$ F_1(x) = x^{d_1} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ F_2(x) = x^{d_2} $\end{document}</tex-math></inline-formula> be power mappings over <inline-formula><tex-math id="M4">\begin{document}$ \mathrm{GF}(q^2) $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M5">\begin{document}$ d_1 = q-1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ d_2 = d_1+\frac{q^2-1}{2} = \frac{(q-1)(q+3)}{2} $\end{document}</tex-math></inline-formula>. In …