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This is a Quantitative Study study.

October 12, 2025Open Access

Permutation polynomials over finite fields from low-degree rational functions

Key Points

Two classes of permutation binomials were identified, expanding the existing knowledge on polynomial structures.
The study introduces six classes of permutation pentanomials, which add to the variety of known polynomials over finite fields.
These newly constructed binomials and pentanomials are proven to be quasi-multiplicative inequivalent to previously known forms.
The findings enhance the understanding of permutation polynomials, particularly in relation to their degree and functionality.

Abstract

This paper considers permutation polynomials over the finite field Fₐℂ in even characteristic by utilizing low-degree permutation rational functions over Fq. As a result, we obtain two classes of permutation binomials and six classes of permutation pentanomials over Fₐℂ. Additionally, we show that the obtained binomials and pentanomials are quasi-multiplicative inequivalent to the known ones in the literature.

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