Florian Enescu, John J. Hull : On subfield-compatible polynomials and a class of Vandermonde-like matrices, 387-397


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