A Note on the Higher-order Nonlinearity of Niho Function

Sun and Wu investigated the lower bound of higher-order nonlinearity of the niho Boolean function f(x)=Trn1n(λxd) over F*2ⁿ; where λ∈F*2ⁿ,[formula] when n ≡ 3 mod 4 in second case of Theorem 3.6 of the paper titled higher-order nonlinearity of niho functions published in Fundamenta Informaticae 137 (2015) 403–412. Unfortunately, the proof of finding the lower bound of higher-order nonlinearities of the niho Boolean function f(x) is not correct in the above mentioned paper. In this paper the author gives the correct proof of lower bound of higher-order nonlinearities of the niho Boolean function f(x).