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Perfect nonlinear functions between two finite abelian groups were studied by Carlet and Ding (J Complex 20:205–244, 2004) and Pott (Discret Math Appl 138:177–193, 2004), which can be regarded as a generalization of bent functions on finite abelian groups studied by Logachev et al. (Discret Math Appl 7:547–564, 1997). Poinsot (J Discret Math Sci Cryptogr 9:349–364, 2006), (Cryptogr Commun 4:1–23,...
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