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In [J. Algebraic Combin. 39 (2014), 457–496] an extension construction of ( n  + 1)-dimensional dual hyperovals using  n -dimensional bilinear dual hyperovals was introduced. Related to this construction is a construction of APN functions in dimension  n  + 1 using two APN functions in dimension  n . In this paper we show that the isomorphism problem for the ( n  + 1)-dimensional extensions can be reduced to the isomorphism problem of the initial  n -dimensional objects. The automorphism problem can be reduced in an analogous way.

Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions