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Permutation trinomials over $\mathbb{F}_{2^m}$: a corrected version

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arxiv 2209.04762 v1 pith:GKPEV6UR submitted 2022-09-11 math.CO math.NT

Danyao Wu , Pingzhi Yuan , Cunsheng Ding , Yuzhen Ma This is my paper · ORCID
classification math.COmath.NT
keywords permutationtrinomialsmathbbsomemathematicsapplicationsareasclasses
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abstract

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we determine all permutation trinomials over $\mathbb{F}_{2^m}$ in Zieve's paper. We prove a conjecture proposed by Gupta and Sharma and obtain some new permutation trinomials over $\mathbb{F}_{2^m}$. Finally, we show that some classes of permutation trinomials with parameters are QM equivalent to some known permutation trinomials.

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  1. Some classes of permutation pentanomials

    math.NT 2025-01 conditional novelty 8.0 of 10

    For every prime p other than 3, this paper builds two large families of five-term permutation polynomials over F_{q^2}, unifying 76 earlier special cases and solving an open problem.

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