Some classes of complete permutation polynomials in the form of (xpm − x + δ )s + axpm + bx over Fp 2m
- Resource Type
- article
- Authors
- Xu Xiaofang; Fan Jinmei
- Source
- Applied Mathematics and Nonlinear Sciences, Vol 8, Iss 1, Pp 1979-1992 (2023)
- Subject
- complete permutation polynomial
finite field
agw criterion
Mathematics
QA1-939
- Language
- English
- ISSN
- 2444-8656
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).