The number of permutation binomials over \({\mathbb F}_{4p+1}\) where \(p\) and \(4p+1\) are primes
The electronic journal of combinatorics, Tome 13 (2006)
We give a characterization of permutation polynomials over a finite field based on their coefficients, similar to Hermite's Criterion. Then, we use this result to obtain a formula for the total number of monic permutation binomials of degree less than $4p$ over ${\Bbb F}_{4p+1}$, where $p$ and $4p+1$ are primes, in terms of the numbers of three special types of permutation binomials. We also briefly discuss the case $q=2p+1$ with $p$ and $q$ primes.
@article{10_37236_1091,
author = {A. Masuda and D. Panario and Q. Wang},
title = {The number of permutation binomials over \({\mathbb {F}_{4p+1}\)} where \(p\) and \(4p+1\) are primes},
journal = {The electronic journal of combinatorics},
year = {2006},
volume = {13},
doi = {10.37236/1091},
zbl = {1121.11077},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1091/}
}
TY - JOUR
AU - A. Masuda
AU - D. Panario
AU - Q. Wang
TI - The number of permutation binomials over \({\mathbb F}_{4p+1}\) where \(p\) and \(4p+1\) are primes
JO - The electronic journal of combinatorics
PY - 2006
VL - 13
UR - http://geodesic.mathdoc.fr/articles/10.37236/1091/
DO - 10.37236/1091
ID - 10_37236_1091
ER -
%0 Journal Article
%A A. Masuda
%A D. Panario
%A Q. Wang
%T The number of permutation binomials over \({\mathbb F}_{4p+1}\) where \(p\) and \(4p+1\) are primes
%J The electronic journal of combinatorics
%D 2006
%V 13
%U http://geodesic.mathdoc.fr/articles/10.37236/1091/
%R 10.37236/1091
%F 10_37236_1091
A. Masuda; D. Panario; Q. Wang. The number of permutation binomials over \({\mathbb F}_{4p+1}\) where \(p\) and \(4p+1\) are primes. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1091
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