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.
Permutation trinomials over $\mathbb{F}_{2^m}$: a corrected version
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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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Some classes of permutation pentanomials
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.