一类三次Bent函数的二阶非线性度

一类三次Bent函数的二阶非线性度 On Second Order Nonlinearity of Cubic Bent Functions 卓泽朋 ZHUO Zepeng 1 first-author 魏仕民 WEI Shimin 1 崇金凤 CHONG Jinfeng 1 王慧 WANG Hui 1 淮北师范大学数学科学学院 淮北师范大学数学科学学院 School of Mathematical Science,Huaibei Normal University School of Mathematical Science,Huaibei Normal University 研究了一类特殊形式的三次Bent函数,通过研究其导数的非线性度的下界,得到了该函数的二阶非线性度的下界.同时,将所得结果与一些特殊类型函数的二阶非线性度的下界进行了比较,这些特殊类型的函数都具有高的一阶非线性度.研究结果表明,所讨论函数的二阶非线性度大于这些已知函数的二阶非线性度的下界. A special form of cubic Bent Boolean function is studied in this paper.By studying the lower bound of the nonlinearity of the derivative of this function,the lower bound on the second order nonlinearity of this form is derived.It is demonstrated that the lower bound of the second order nonlinearity of the function of this form is larger than those obtained for several known classes of Boolean functions having high first order nonlinearities. 布尔函数 Bent函数 二阶非线性度 导数 Boolean function Bent function second order nonlinearity derivative 10.14188/j.1671-8836.2013.01.016 TN918.1 安徽省自然科学基金项目（1208085QF119）;安徽高校省级自然科学基金研究项目（KJ2012Z353） 2013-01-01 2021-04-01 1 59