Extended Affine and CCZ Equivalence up to Dimension 4

Marcus Brinkmann

A complete classification of all vectorial boolean functions in up to dimension 4, up to extended affine and CCZ equivalence. Work done as part of my diploma thesis in 2008, and since then cited as personal communication.


Abstract

For all vectorial boolean functions up to dimension 4, we present canonical representatives for all extended affine (EA) and CCZ equivalence classes. We include the size of each class, as well as its algebraic degree and extended Walsh spectrum. We also answer the following questions: How large are these classes? Which of these classes contain bijective functions? And how are these classes grouped into CCZ equivalence classes?

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tags: ccz equivalence, extended affine equivalence, vectorial boolean functions