Improved Lower Bounds for Permutation Arrays Using Permutation Rational Functions

@inproceedings{Bereg2020ImprovedLB,
  title={Improved Lower Bounds for Permutation Arrays Using Permutation Rational Functions},
  author={S. Bereg and Brian Malouf and L. Morales and Thomas Stanley and I. H. Sudborough},
  booktitle={WAIFI},
  year={2020}
}
We consider rational functions of the form $V(x)/U(x)$, where both $V(x)$ and $U(x)$ are polynomials over the finite field $\mathbb{F}_q$. Polynomials that permute the elements of a field, called {\it permutation polynomials ($PPs$)}, have been the subject of research for decades. Let ${\mathcal P}^1(\mathbb{F}_q)$ denote $\mathbb{Z}_q \cup \{\infty\}$. If the rational function, $V(x)/U(x)$, permutes the elements of ${\mathcal P}^1(\mathbb{F}_q)$, it is called a {\em permutation rational… Expand

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