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- W4288725053 abstract "Permutation polynomials with coefficients 1 over finite fields attract researchers' interests due to their simple algebraic form. In this paper, we first construct four classes of fractional permutation polynomials over the cyclic subgroup of $ mathbb{F}_{2^{2m}} $. From these permutation polynomials, three new classes of permutation polynomials with coefficients 1 over $ mathbb{F}_{2^{2m}} $ are constructed, and three more general new classes of permutation polynomials with coefficients 1 over $ mathbb{F}_{2^{2m}} $ are constructed using a new method we presented recently. Some known permutation polynomials are the special cases of our new permutation polynomials. Furthermore, we prove that, in all new permutation polynomials, there exists a permutation polynomial which is EA-inequivalent to known permutation polynomials for all even positive integer $ m $. This proof shows that EA-inequivalent permutation polynomials over $ mathbb{F}_{q} $ can be constructed from EA-equivalent permutation polynomials over the cyclic subgroup of $ mathbb{F}_{q} $. From this proof, it is obvious that, in all new permutation polynomials, there exists a permutation polynomial of which algebraic degree is the maximum algebraic degree of permutation polynomials over $ mathbb{F}_{2^{2m}} $." @default.
- W4288725053 created "2022-07-30" @default.
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- W4288725053 date "2022-07-27" @default.
- W4288725053 modified "2023-10-16" @default.
- W4288725053 title "New classes of permutation polynomials with coefficients 1 over finite fields" @default.
- W4288725053 doi "https://doi.org/10.48550/arxiv.2207.13335" @default.
- W4288725053 hasPublicationYear "2022" @default.
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