Cycle structure of permutation functions over finite fields and their applications

Amin Sakzad; Mohammad-Reza Sadeghi; Daniel Panario

doi:10.3934/amc.2012.6.347

Article Contents

2012, Volume 6, Issue 3: 347-361. Doi: 10.3934/amc.2012.6.347

This issue Previous Article Structural properties of binary propelinear codes Next Article Computation of cross-moments using message passing over factor graphs

Cycle structure of permutation functions over finite fields and their applications

1.
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran
2.
School of Mathematics and Statistics, Carleton University, Ottawa

Received: October 31, 2011

Revised: April 30, 2012

Published: July 2012

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Abstract

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.

Keywords:

Interleavers and permutation functions over finite fields.

Mathematics Subject Classification: Primary: 12E20, 12E05, 94B60; Secondary: 94A05, 94A24, 94B10.

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