# 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

#### References

SHOWING 1-10 OF 30 REFERENCES
New lower bounds for permutation arrays using contraction
• Mathematics, Computer Science
• Des. Codes Cryptogr.
• 2019
Extending permutation arrays: improving MOLS bounds
• Mathematics, Computer Science
• Des. Codes Cryptogr.
• 2017
New Constructions of Permutation Arrays
• Computer Science, Mathematics
• ArXiv
• 2008
Constructing permutation arrays from groups
• Mathematics, Computer Science
• Des. Codes Cryptogr.
• 2018
Permutation codes invariant under isometries
• Mathematics, Computer Science
• Des. Codes Cryptogr.
• 2015
Constructing permutation arrays using partition and extension
• Mathematics, Computer Science
• Des. Codes Cryptogr.
• 2020
New Lower Bounds for Permutation Codes Using Linear Block Codes
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2020
PERMUTATION POLYNOMIALS OF DEGREE 8 OVER FINITE FIELDS OF ODD CHARACTERISTIC
• X. Fan
• Mathematics
• Bulletin of the Australian Mathematical Society
• 2019