1. Classification of some quadrinomials over finite fields of odd characteristic.
- Author
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Özbudak, Ferruh and Gülmez Temür, Burcu
- Subjects
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FINITE fields , *PERMUTATIONS , *CLASSIFICATION , *PERMUTATION groups - Abstract
In this paper, we completely determine all necessary and sufficient conditions such that the polynomial f (x) = x 3 + a x q + 2 + b x 2 q + 1 + c x 3 q , where a , b , c ∈ F q ⁎ , is a permutation quadrinomial of F q 2 over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where c h a r (F q) = 2 and finally, in [16] , Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial x 3 + a x q + 2 + b x 2 q + 1 + c x 3 q , where c h a r (F q) = 3 , 5 and a , b , c ∈ F q ⁎ and proposed some new classes of permutation quadrinomials of F q 2 . In particular, in this paper we classify all permutation polynomials of F q 2 of the form f (x) = x 3 + a x q + 2 + b x 2 q + 1 + c x 3 q , where a , b , c ∈ F q ⁎ , over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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