A new method for solving the equation x^d+(x+1)^d=b in \mathbbF_q⁴ where d=q³+q²+q-1

2023/05/18 by Liqin Qian, Qian, Liqin, Minjia Shi +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2305.10671

openalex publication_date 2023/05/18 · openalex created_date 2023/05/21 · openalex updated_date 2026/07/28

Abstract

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 \mathbbF_q⁴, where n is a positive integer, q=2ⁿ and d=q³+q²+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.

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