  In 1980 Alltop produced a family of cubic phase sequences that nearly meet
the Welch bound for maximum non-peak correlation magnitude. This family of
sequences were shown by Wooters and Fields to be useful for quantum state
tomography. Alltop's construction used a function that is not planar, but whose
difference function is planar. In this paper we show that Alltop type functions
cannot exist in fields of characteristic 3 and that for a known class of planar
functions, $x^3$ is the only Alltop type function.
