# Permutation polynomials

Gary L. Mullen, Qiang Wang

Research output: Chapter in Book/Report/Conference proceedingChapter

11 Citations (Scopus)

### Abstract

For odd q, f(x) = x(q+1)/2 + ax is a PP of Fq if and only if a2- 1 is a nonzero square in Fq. Moreover, the polynomial f(x) + cx is a PP of Fq for (q - 3)/2 values of c ? Fq . The polynomial xr(f(xd))(q-1)/d is a PP of Fq if (r, q - 1) = 1, d q - 1, and f(xd) has no nonzero root in Fq.

Original language English (US) Handbook of Finite Fields CRC Press 215-240 26 9781439873823 9781439873786 https://doi.org/10.1201/b15006 Published - Jan 1 2013

### Fingerprint

Permutation Polynomial
Polynomials
Polynomial
Odd
Roots
If and only if

### All Science Journal Classification (ASJC) codes

• Computer Science(all)
• Mathematics(all)

### Cite this

Mullen, G. L., & Wang, Q. (2013). Permutation polynomials. In Handbook of Finite Fields (pp. 215-240). CRC Press. https://doi.org/10.1201/b15006
Mullen, Gary L. ; Wang, Qiang. / Permutation polynomials. Handbook of Finite Fields. CRC Press, 2013. pp. 215-240
@inbook{82d0fbd5917c41edb6f041ff6a81d1a7,
title = "Permutation polynomials",
abstract = "For odd q, f(x) = x(q+1)/2 + ax is a PP of Fq if and only if a2- 1 is a nonzero square in Fq. Moreover, the polynomial f(x) + cx is a PP of Fq for (q - 3)/2 values of c ? Fq . The polynomial xr(f(xd))(q-1)/d is a PP of Fq if (r, q - 1) = 1, d q - 1, and f(xd) has no nonzero root in Fq.",
author = "Mullen, {Gary L.} and Qiang Wang",
year = "2013",
month = "1",
day = "1",
doi = "10.1201/b15006",
language = "English (US)",
isbn = "9781439873786",
pages = "215--240",
booktitle = "Handbook of Finite Fields",
publisher = "CRC Press",

}

Mullen, GL & Wang, Q 2013, Permutation polynomials. in Handbook of Finite Fields. CRC Press, pp. 215-240. https://doi.org/10.1201/b15006

Permutation polynomials. / Mullen, Gary L.; Wang, Qiang.

Handbook of Finite Fields. CRC Press, 2013. p. 215-240.

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Permutation polynomials

AU - Mullen, Gary L.

AU - Wang, Qiang

PY - 2013/1/1

Y1 - 2013/1/1

N2 - For odd q, f(x) = x(q+1)/2 + ax is a PP of Fq if and only if a2- 1 is a nonzero square in Fq. Moreover, the polynomial f(x) + cx is a PP of Fq for (q - 3)/2 values of c ? Fq . The polynomial xr(f(xd))(q-1)/d is a PP of Fq if (r, q - 1) = 1, d q - 1, and f(xd) has no nonzero root in Fq.

AB - For odd q, f(x) = x(q+1)/2 + ax is a PP of Fq if and only if a2- 1 is a nonzero square in Fq. Moreover, the polynomial f(x) + cx is a PP of Fq for (q - 3)/2 values of c ? Fq . The polynomial xr(f(xd))(q-1)/d is a PP of Fq if (r, q - 1) = 1, d q - 1, and f(xd) has no nonzero root in Fq.

UR - http://www.scopus.com/inward/record.url?scp=85006343815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006343815&partnerID=8YFLogxK

U2 - 10.1201/b15006

DO - 10.1201/b15006

M3 - Chapter

AN - SCOPUS:85006343815

SN - 9781439873786

SP - 215

EP - 240

BT - Handbook of Finite Fields

PB - CRC Press

ER -

Mullen GL, Wang Q. Permutation polynomials. In Handbook of Finite Fields. CRC Press. 2013. p. 215-240 https://doi.org/10.1201/b15006