The compositional inverse of a class of bilinear permutation polynomials over finite fields of characteristic 2

TL;DR

This paper derives the compositional inverses of a recently constructed class of bilinear permutation polynomials over finite fields of characteristic 2, generalizing previous results.

Contribution

It provides a direct method to find inverses of a broad class of bilinear permutation polynomials using finite field decomposition.

Findings

Explicit formulas for inverses of the polynomials

Generalization of previous inverse results

Application of finite field decomposition techniques

Abstract

A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them based on a direct sum decomposition of the finite field. The result generalizes that in [R.S. Coulter, M. Henderson, The compositional inverse of a class of permutation polynomials over a finite field, Bull. Austral. Math. Soc. 65 (2002) 521-526].