8元多输出旋转对称弹性函数的构造与计数

Construction and count of multi-output rotation symmetric resilient functions with 8 input variables

在2~r个变元的多输出旋转对称平衡函数和弹性函数存在的条件下,研究了输出变量维数的取值问题。根据输出变量的不同维数,基于弹性函数和正交表大集间的等价关系,给出了8元多输出平衡函数的计数结果,在此基础上进一步研究了8元多输出旋转对称1-弹性函数的构造与计数方法,将这类函数的构造问题转化为方程组的求解问题。

The value ranges of the number of output variables were determined respectively under the existence of multi-output rotation symmetric balanced functions and resilient functions with2r input variables.Based on the equivalence between the resilient functions and large sets of orthogonal arrays,some results on the construction and count of multi-output rotation symmetric balanced functions with8input variables were presented according to the different dimensions of output vectors,and construction and count of multi-output rotation symmetric1-resilient functions with8input variables were also studied.Besides,constructions of multi-output rotation symmetric resilient functions are transformed into the problem of solving a system of equations.