Let and be finite fields of characteristic , where is prime. This note investigates polynomial representations of functions that map to 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.

Key Words:interpolation, Frobenius permutation, cycle bases, Vandermonde matrices.

2010 Mathematics Subject Classification: 12E20, 15B99