Structured Groebner basis search in a 40-dimensional self-equivalence subspace of functions over F_{2^8} yields 566 quadratic APN functions in six classes, four of which are absent from prior databases of millions of instances.
The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes,
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Quadratic APN Functions in Dimension 8 via Gr\"obner Basis Search in a Self-Equivalence Subspace
Structured Groebner basis search in a 40-dimensional self-equivalence subspace of functions over F_{2^8} yields 566 quadratic APN functions in six classes, four of which are absent from prior databases of millions of instances.