  In this work we establish some new interleavers based on permutation
functions. The inverses of these interleavers are known over a finite field
$\mathbb{F}_q$. For the first time M\"{o}bius and R\'edei functions are used to
give new deterministic interleavers. Furthermore we employ Skolem sequences in
order to find new interleavers with known cycle structure. In the case of
R\'edei functions an exact formula for the inverse function is derived. The
cycle structure of R\'edei functions is also investigated. The self-inverse and
non-self-inverse versions of these permutation functions can be used to
construct new interleavers.
