On the number of permutation polynomials over a finite field
Rings and Algebras
2013-12-18 v2
Abstract
We find a formula for the number of permutation polynomials of degree q-2 over a finite field Fq, which has q elements, in terms of the permanent of a matrix. We write down an expression for the number of permutation polynomials of degree q-2 over a finite field Fq, using the permanent of a matrix whose entries are pth roots of unity and using this obtain a nontrivial bound for the number. Finally, we provide a formula for the number of permutation polynomials of degree d less than q-2.
Keywords
Cite
@article{arxiv.1310.7691,
title = {On the number of permutation polynomials over a finite field},
author = {Kwang-Yon Kim and Ryul Kim},
journal= {arXiv preprint arXiv:1310.7691},
year = {2013}
}
Comments
10 pages