APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials
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n = 6
The polynomial
x3 + α17(x17 + x18 + x20 + x24) + α14( Tr( α52x3 + α6x5 + α19x7 + α28x11 + α2x13) + (α2x)9 + (α2x)18 + (α2x)36 + x21 + x42)
where is α is primitive in GF(2^6), is the only known example of an APN function CCZ-inequivalent to a monomial or quadratic function [1][2] A Magma implementation of the polynomial is available.