A note on planar functions of degree p 2

We determined planar functions which are power functions on the additive group GF(p 2 ) where p is an odd prime. This result asserts that a planar power function on the additive group GF(p 2n ) shoud be of the form f(x) = x t(p 2 1)+2pi for a suitable non-negative integer t and i 2 {0,1}.