Cycle structure of permutation functions over finite fields and their applications

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 Möbius and Rédei 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 Rédei functions an exact formula for the inverse function is derived. The cycle structure of Rédei functions is also investigated. The self-inverse and non-self-inverse versions of these permutation functions can be used to construct new interleavers.

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