Complete Characterization of a Class of Permutation Trinomial in Characteristic Five

Date

2024-02-01

Author

Grassl, Markus
Özbudak, Ferruh
Özkaya, Buket
Gülmez Temür, Burcu

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In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form f (x) = x4q+1 + λ1 x5q + λ2 x q+4 over the finite field F5k , which are not quasi- multiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on λ1, λ2 ∈ F5k so that f (x) is a permutation monomial, binomial, or trinomial of F5 2k .

URI

https://hdl.handle.net/11511/108596

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Graduate School of Applied Mathematics, Article