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Regular complete permutation polynomials over quadratic extension fields

Wei LuXia WuYufei WangXiwang Cao
Dec 2022
摘要
Let $r\geq 3$ be any positive integer which is relatively prime to $p$ and$q^2\equiv 1 \pmod r$. Let $\tau_1, \tau_2$ be any permutation polynomials over$\mathbb{F}_{q^2},$ $\sigma_M$ is an invertible linear map over$\mathbb{F}_{q^2}$ and $\sigma=\tau_1\circ\sigma_M\circ\tau_2$. In this paper,we prove that, for suitable $\tau_1, \tau_2$ and $\sigma_M$, the map $\sigma$could be $r$-regular complete permutation polynomials over quadratic extensionfields.
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