The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. By investigating the lower bound of the nonlinearity of the derivative of the function f, this paper tightens the lower bound of the second-order nonlinearity of a class of Boolean functions over F2n{F_{2^n}} with high nonlinearity in the form f(x) = tr(λ x d ), where l Î F2r*, d=22r+2r+1{lambdain F_{2^r}^*, d=2^{2r}+2^{r}+1} and n = 4r.
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机译：布尔函数的r阶非线性是与流和分组密码的某些攻击相关的重要密码学准则。它在编码理论中也非常有用，因为它与Reed-Muller码的覆盖半径有关。通过研究函数f的导数的非线性下界，收紧了F 2 n {F_ {2 ^ n}}，具有高度非线性，形式为f（x）= tr（λx d ），其中lÎF 2 r * ，d = 2 2r +2 r +1 {lambdain F_ {2 ^ r} ^ *，d = 2 ^ {2r} + 2 ^ {r} +1}，n = 4r。
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