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Enumerating permutation polynomials. (English) Zbl 1401.11155
Summary: We consider the problem of enumerating polynomials over \(\mathbb{F}_q\), that have certain coefficients prescribed to given values and permute certain substructures of \(\mathbb{F}_q\). In particular, we are interested in the group of \(N\)-th roots of unity and in the submodules of \(\mathbb{F}_q\). We employ the techniques of Konyagin and Pappalardi to obtain results that are similar to their results in [S. Konyagin and F. Pappalardi, Finite Fields Appl. 12, No. 1, 26–37 (2006; Zbl 1163.11350)]. As a consequence, we prove conditions that ensure the existence of low-degree permutation polynomials of the mentioned substructures of \(\mathbb{F}_q\).
MSC:
11T06 Polynomials over finite fields
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