Quadratic APN functions as subspaces of alternating bilinear forms

Proceedings of the Contact Forum Coding Theory and Cryptography III at The Royal Flemish Academy of Belgium for Science and the Arts 2009, (2011), 11-24.


In this note we illuminate and apply the equivalence of quadratic APN functions to certain subspaces of alternating bilinear forms. These subspaces can be characterized by the rank-distance of the dual subspace, or equivalently, as the subspaces of $\bigwedge^2$ GF(2)m avoiding the variety of elements of rank 2. Or, in the geometric language, as subspaces external (or skew) to the line Grassmannian.

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