New results on permutation binomials of finite fields

Hou, Xiang‐dong; Lavorante, Vincenzo Pallozzi

doi:10.1016/j.ffa.2023.102179

Cited by 5 publications

(2 citation statements)

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“…This is a contradiction. It is easy to check that H(x) is not linearly related to x(x − α) 10 . Based on the above discuss, we conclude that H(x) is not a permutation polynomial over F q .…”

Section: Nonexistence Permutation Trinomials Of the Formmentioning

confidence: 99%

“…As usual, x r h(x) q−1 = x r h(x) q h(x) is a rational function on µ q+1 . Specially, when x r h(x) q−1 is monomial on the subsets of µ q+1 , Hou [10] gave a general method to construct permutation polynomials of the form x r h(x q−1 ). Furthermore, Zieve [21] characterized the degree-one bijection from µ q+1 to F q ∪ {∞} as follows:…”

Section: Introductionmentioning

confidence: 99%

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Some results on permutation polynomials over finite fields

Qin

2023

Preprint

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Permutation polynomials is a hot topic in finite fields. Permutation polynomials with the form $x^rh(x^{q-1})$ of ${\bf F}_{q^{2}}$ have been studied extensively. In this paper, we build a general relation between permutation polynomials having the form $x^rh(x^{q-1})$ over ${\bf F}_{q^{2}}$ and permutation rational functions over ${\bf F}_{q}$. For $p=11, 13$ and $q=p^k$, by using the exceptional polynomials of degrees 11 and 13 of ${\bf F}_{q}$, we focus on studying the permutation properties of trinomials $x^{q+10}(ax^{10(q-1)}+x^{9(q-1)}+1)$ and $x^{q+6}(ax^{9(q-1)}+x^{5(q-1)}+1), x^{q+12}(ax^{12(q-1)}+x^{11(q-1)}+1)$ over ${\bf F}_{q^{2}}$. Conversely, we show an approach to using permutation polynomials over ${\bf F}_{q}$ to get permutation polynomials over ${\bf F}_{q^2}$.

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Section: Nonexistence Permutation Trinomials Of the Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%