Permutation polynomials, projective polynomials, and bijections between ${\mu }_{\frac{q^n-1}{q-1}}$ and $PG(n-1,q)$

Tong Lin, Qiang Wang

Using arbitrary bases for the finite field ${\mathbb{F}}_{q^n}$ over ${\mathbb{F}}_q$, we obtain the generalized Möbius transformations (GMTs), which are a class of bijections betwee…