A new method for solving the equation x^d+(x+1)^d=b in 𝔽_q^4 where d=q^3+q^2+q-1

05/18/2023

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by   Liqin Qian, et al.

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In this paper, we give a new method answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski about the equation x^d+(x+1)^d=b in 𝔽_q^4, where n is a positive integer, q=2^n and d=q^3+q^2+q-1. In particular, we directly determine the differential spectrum of this power function x^d using methods different from those in the literature. Compared with the methods in the literature, our method is more direct and simple.