大偶数元上几乎最优弹性布尔函数的构造
Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables
摘要：
本文描述了一种构造非线性弹性布尔函数的方法。通过使用少量变量的几组不相交谱函数，可以构造大量偶数变量的几乎最优弹性函数。它表明，给定任何$m$，可以构造无穷多个$n$ -变量（$n$甚至），$m$ -弹性函数的非线性$>2^{n-1}-2^{n/2}$。得到了一大类未知的高度非线性弹性函数。然后提出了一种优化构造函数度的方法。最后给出了主要结构的改进方案。
英文摘要：
In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number of variables can be constructed. It is shown that given any $m$, one can construct infinitely many $n$-variable ($n$ even), $m$-resilient functions with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of highly nonlinear resilient functions which were not known are obtained. Then one method to optimize the degree of the constructed functions is proposed. Last, an improved version of the main construction is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
