Regular complete permutation polynomials over quadratic extension fields

Wei Lu; Xia Wu; Xiwang Cao; Yufei Wang

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Regular complete permutation polynomials over quadratic extension fields

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arxiv 2212.13674 v1 pith:UDA3VQDP submitted 2022-12-28 cs.IT math.ITmath.NT

Regular complete permutation polynomials over quadratic extension fields

Wei Lu , Xia Wu , Yufei Wang , Xiwang Cao This is my paper

classification cs.IT math.ITmath.NT

keywords sigmapermutationpolynomialscirccompleteextensionfieldsmathbb

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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 extension fields.

Regular complete permutation polynomials over quadratic extension fields

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