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Several classes of complete permutation polynomials (CPPs) in the form of (<italic>xpm</italic> − <italic>x</italic>+ <italic>δ</italic> )<italic>s </italic>+ <italic>axpm</italic> + <italic>bx</italic> over <italic>Fp</italic>2<italic>m</italic> are described in this paper. For fractional exponent <italic>s</italic>, the permutation properties of the given polynomials are proved by the AGW criterion and for determining the bijectivity of the corresponding piecewise functions. For exponent <italic>s</italic>satisfying <italic>s</italic>= <italic>i</italic>(<italic>pm</italic> − 1) + <italic>pj</italic>, the main proofs here depend on the AGW criterion and the quantity of solutions for certain linearised equations. Several results generalise some earlier results on permutation polynomials (PPs).
</abstract>

Several classes of complete permutation polynomials (CPPs) in the form of (xpm − x+ δ )s + axpm + bx over Fp2m are described in this paper. For fractional exponent s, the permutation properties of the given polynomials are proved by the AGW criterion and for determining the bijectivity of the corresponding piecewise functions. For exponent ssatisfying s= i(pm − 1) + pj, the main proofs here depend on the AGW criterion and the quantity of solutions for certain linearised equations. Several results generalise some earlier results on permutation polynomials (PPs).

Some classes of complete permutation polynomials in the form of (<italic>xpm</italic> − <italic>x</italic> + <italic>δ</italic> )<italic>s</italic> + <italic>axpm</italic> + <italic>bx</italic> over <italic>Fp</italic> 2<italic>m</italic>

Applied Mathematics and Nonlinear Sciences

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Some classes of complete permutation polynomials in the form of ( −  +  ) +  +  over  

Several classes of complete permutation polynomials (CPPs) in the form of (xpm − x+ δ )s + axpm + bx over Fp2m are described in this paper. For fractional...

Some classes of complete permutation polynomials in the form of (x^{p^m} − x + δ )^s + ax^{p^m} + bx over F_{_p} _2m

Online veröffentlicht: 15. März 2022

Seitenbereich: 1979 - 1992

Eingereicht: 10. Sept. 2021

Akzeptiert: 27. Nov. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00132

Schlüsselwörter
complete permutation polynomial, finite field, AGW criterion

© 2023 Xiaofang Xu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Some classes of complete permutation polynomials in the form of (xpm − x + δ )s + axpm + bx over Fp 2m

Online veröffentlicht: 15. März 2022

Seitenbereich: 1979 - 1992

Eingereicht: 10. Sept. 2021

Akzeptiert: 27. Nov. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00132

Schlüsselwörtercomplete permutation polynomial, finite field, AGW criterion

© 2023 Xiaofang Xu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Some classes of complete permutation polynomials in the form of (x^{p^m} − x + δ )^s + ax^{p^m} + bx over F_{_p} _2m

Schlüsselwörter
complete permutation polynomial, finite field, AGW criterion