Abstract
A function \(f:\mathbb{F}_p^{\; n}\to\mathbb{F}_p^{\; n}\) is called planar if x↦f(x + a) − f(x) is a permutation for all \(a\ne 0\). In this note we characterize planar functions within a class of functions \(\mathbb{F}_{p}^{\; 2m}\to\mathbb{F}_{p}^{\; 2m}\) via the planarity of functions \(\mathbb{F}_p^{\; m}\to\mathbb{F}_p^{\; m}\). This class contains some interesting families of planar functions. The proof uses character theoretic arguments.
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The second author is partially supported by Natural Science Foundation of China (No.61070215) and China Scholarship Council.
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Pott, A., Zhou, Y. A character theoretic approach to planar functions. Cryptogr. Commun. 3, 293–300 (2011). https://doi.org/10.1007/s12095-011-0044-4
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DOI: https://doi.org/10.1007/s12095-011-0044-4