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

Laigle-Chapuy constructed a class of permutation polynomials over a finite field of characteristic 2, which includes several other known classes. In this paper, we determine the compositional inverses of all Laigle-Chapuy's permutation polynomials. Our method is based on a direct sum decomposition of the finite field.