Abstract
A function f : GF(2 r ) ? GF(2 r ) is called crooked if the sets {f(x) + f(x + a)|x ? GF(2 r )} is an affine hyperplane for any nonzero a ? GF(2 r ). We prove that a crooked binomial function f(x) = x d + ux e defined on GF(2 r ) satisfies that both exponents d, e have 2-weights at most 2.
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