均衡弹性函数的结构与弹性阶

Structures and Resilient Orders of Balanced Resilient Functions

弹性函数是相关免疫布尔函数的自然推广。本文讨论均衡弹性函数 ,得到以下结果 :给出了均衡弹性函数的一种结构 ,并因此得到了由均衡 (n ,m ,2t)弹性函数构造均衡 (n +1,m ,2t+1)弹性函数的非线性方法 ;证明了均衡线性函数的弹性阶等于对应线性分组码的码字最小重最减 1,且弹性阶上确界常常能由非线性函数所达到。

Resilient function is a natural generalization of correlation immunity Boolean function.This paper discusses balanced resilient functions,with following results:a kind of structure of balanced resilient functions is presented,and therefore a method is given which constructs balanced ( n+1,m,2t+1 ) resilient functions from balanced ( n,m,2t ) resilient functions;a proposition is given and proved that the resilient order of the balanced linear function equals the mini-weight of corresponding block code minus one,and the supremum of this order can often be reached by non-linear functions.