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

In [5] 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 Lambda PN functions in dimension n + 1 using two Lambda PN 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.