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On a Case of Family Resemblance of Reed-Muller and Reed-Muller-Fourier Transforms
Claudio Moraga, Radomir S. Stanković and Milena Stanković
Let 𝑝 be an odd prime. We review the characterization of 𝑝-valued Maiorana-McFarland bent functions with the Reed-Muller and the Reed-Muller-Fourier Transforms. We show that both transforms generate the same characterization and, based on the orthogonality of vectors, we prove why this is possible. Following the Language Philosopher Ludwig von Wittgenstein we consider this as a case of Family Resemblance.
Keywords: Orthogonality over finite fields, Maiorana-McFarland bent functions, Reed-Muller and Reed-Muller-Fourier transforms