Let
![$K$](img2.png)
and
![$L$](img3.png)
be finite fields of characteristic
![$p$](img4.png)
, where
![$p$](img4.png)
is prime. This note investigates polynomial representations of functions that map
![$K$](img2.png)
to
![$L$](img3.png)
by providing a canonical basis for the set of minimally represented such polynomials. This interpolation problem leads to a class of Vandermonde-like matrices that are also fully described. This problem has potential applications to the hardware design of arithmetic circuits.