Rayleigh quotients of Dillon's functions

04/08/2023

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by   Aditi Kar Gangopadhyay, et al.

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The Walsh–Hadamard spectrum of a bent function uniquely determines a dual function. The dual of a bent function is also bent. A bent function that is equal to its dual is called a self-dual function. The Hamming distance between a bent function and its dual is related to its Rayleigh quotient. Carlet, Danielsen, Parker, and Sole studied Rayleigh quotients of bent functions in 𝒫S_ap, and obtained an expression in terms of a character sum. We use another approach comprising of Desarguesian spreads to obtain the complete spectrum of Rayleigh quotients of bent functions in 𝒫𝒮_ap.