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- W3119443344 abstract "For a positive integer k and a linearized polynomial L(X), polynomials of the form $P(X)=G(X)^{k}-L(X) in {mathbb F}_{q^{n}}[X]$ are investigated. It is shown that when L has a non-trivial kernel and G is a permutation of $mathbb {F}_{q^{n}}$ , then P(X) cannot be a permutation if $gcd (k,q^{n}-1)>1$ . Further, necessary conditions for P(X) to be a permutation of $mathbb {F}_{q^{n}}$ are given for the case that G(X) is an arbitrary linearized polynomial. The method uses plane curves, which are obtained via the multiplicative and the additive structure of $mathbb {F}_{q^{n}}$ , and their number of rational affine points." @default.
- W3119443344 created "2021-01-18" @default.
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- W3119443344 date "2021-01-05" @default.
- W3119443344 modified "2023-09-27" @default.
- W3119443344 title "Permutations polynomials of the form G(X)k − L(X) and curves over finite fields" @default.
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- W3119443344 doi "https://doi.org/10.1007/s12095-020-00465-9" @default.
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