Automorphisms and isomorphisms of some p-ary bent functions

In the predecessor to this paper Dempwolff (Comm Algebra 34(3):1077-1131,2006), group-theoretic methods were used to solve automorphism and equivalence questions for (certain) ordinary bent functions, i.e., bent functions over F-2. Here, we consider the same problems forp-ary bent functions,pan odd prime and solve these questions for functions analogous to those which appear in Dempwolff (Comm Algebra 34(3):1077-1131,2006). Although our general analysis is similar to the approach of Dempwolff (Comm Algebra 34(3):1077-1131,2006), it turns out that the odd characteristic leads to simplifications: Often, the double derivative can be computed (cf. Lemma 2.10) and factorizations of the automorphism group (cf. Lemma 2.3) can be established resulting in restrictions for automorphisms and equivalence maps.