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 [1939]. 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 languageEnglish (US)
Title of host publicationHandbook of Finite Fields
PublisherCRC Press
Pages215-240
Number of pages26
ISBN (Electronic)9781439873823
ISBN (Print)9781439873786
DOIs
StatePublished - 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
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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

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