On planar functions of elementary abelian \(p\)-group type (Q949102)

The authors give many examples and known theorems on planar functions of abelian \(p\)-group type. They prove affine planes corresponding to quadratic planar functions over \(\mathbb{F}_{p^n}\) are semifield planes, and determine affine planes corresponding to planar function \(f(x)= x^{10}-\alpha x^6- \alpha^2x^2\) by Ding and Yuan. Moreover, they calculate explicit shapes of planar functions from the square mapping of almost all known finite commutative fields, i.e. Dickson, Cohen-Ganley, Ganley, Penttila-Williams, Coulter-Matthews and Ding-Yuan semifields.