Quadratic binomials F(x)=x^{d1}+x^{d2} over F_{2^n} (n=2m) with maximal bent components are affine equivalent to x^{2^m+1} or x^{2^i}(x+x^{2^m}) under wt_2(d_i)≤2, ℓ(n)>m, and gcd(d1,d2,2^m-1)>1.
Bounds on the nonlinearity of differentially uniform functions by means of their image set size, and on their distance to affine functions
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On quadratic binomial vectorial functions with maximal bent components
Quadratic binomials F(x)=x^{d1}+x^{d2} over F_{2^n} (n=2m) with maximal bent components are affine equivalent to x^{2^m+1} or x^{2^i}(x+x^{2^m}) under wt_2(d_i)≤2, ℓ(n)>m, and gcd(d1,d2,2^m-1)>1.