弹性函数的平方和指标

Sum-of-Squares Indicator of Resilient Functions

Son等给出了0-弹性函数(平衡函数)的平方和指标的下界。Maitra给出了m-弹性函数的平方和指标的下界。基于Sarkar和Maitra关于m-弹性函数的Walsh谱的结果[1],一个m-弹性函数的平方和指标的新的下界被给出。可以将这3个下界结合起来,针对特定的m(m大于或等于0,小于或等于m-3),给出相应的下界。然后发现,在许多情形下,新下界比上面提到的两个下界要紧一些。最后证明,当m等于n-3时,m-弹性函数的平方和指标要么是23n-2,要么23n。m等于是n-2,n-1时,m-弹性函数的平方和指标是确定的,它们是23n。

Son et al. give the lower bound on the sum of squares indicator of 0-resilient function(balanced function). Maitra gives the lower bound on the sum of squares indicator of m-resilient function. Based on the result of Walsh spectrum of m-resilient function given by Sarkar and Maitra[1],a new lower bound on the sum of squares indicator of m-resilient function is given. By combining the new lower bound with the two old lower bounds,the corresponding lower bound is obtained for particular m(m is no less than 0 and not greater than m-3). Then,it is found that in many cases,the new lower bound is tighter than the above mentioned two old lower bounds. Finally,it is shown that when m is equal to n-3,the sum of squares indicator of m-resilient function is 23n-2 or 23n,when m is equal to n-2 or n-1,the sum of squares indicator of m-resilient function is 23n.