A NOTE ON INTERPOLATION OF PERMUTATIONS OF A SUBSET OF A FINITE FIELD

We determine several variants of the classical interpolation formula for finite fields which produce polynomials that induce a desirable mapping on the nonspecified elements, and without increasing the number of terms in the formula. As a corollary, we classify those permutation polynomials over a finite field which are their own compositional inverse, extending work of C. Wells.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.