Classification of p-ary self dual quadratic bent functions, p odd

Let p be an odd prime. We classify all self dual quadratic bent functions from Fpn to Fp under the action of the orthogonal group O(n,Fp). The sizes of the O(n,Fp)-orbits of such self dual bent functions are explicitly determined. These results are obtained through the following steps: 1. n×n symmetric matrices A over Fp satisfying A2=cI (c∈Fp⁎) are classified under the conjugation by O(n,Fp). 2. For each representative A in step 1, the orbits of ker(A−I) under the action of centO(n,Fp)(A) are determined. 3. The sizes of the orbits in steps 1 and 2 are computed.