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Fourier transforms and bent functions on finite groups. (English) Zbl 1393.43003
The authors introduce a dual basis on a finite nonabelian group, determined by its unitary irreducible representations. Furthermore they define the Fourier transform on such a basis, and obtain characterizations of bent, dual and perfect nonlinear functions by their Fourier transforms.
MSC:
 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 20C15 Ordinary representations and characters
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References:
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