A new construction of rotation symmetric bent functions with maximal algebraic degree

In this paper, for any even integer begin{document}$ n = 2mge4 $end{document} , a new construction of begin{document}$ n $end{document} -variable rotation symmetric bent function with maximal algebraic degree begin{document}$ m $end{document} is given asbegin{document}$ f(x_0,x_1cdots,x_{n-1}) = bigopluslimits_{i = 0}^{m-1}(x_ix_{m+i})oplus bigopluslimits_{i = 0}^{n-1}(x_ix_{i+1}cdots x_{i+m-2} overline{x_{i+m}} ), $end{document}whose dual function isbegin{document}$ widetilde{f}(x_0,x_1cdots,x_{n-1}) = bigopluslimits_{i = 0}^{m-1}(x_ix_{m+i})oplus bigopluslimits_{i = 0}^{n-1}(x_ix_{i+1}cdots x_{i+m-2} overline{x_{i+n-2}} ), $end{document}where begin{document}$ overline{x_{i}} = x_{i}oplus 1 $end{document} and the subscript of begin{document}$ x $end{document} is modulo begin{document}$ n $end{document} .