Related papers: On the differential and Walsh spectra of $x^{2q+1}$ over $\mathbb{F}

On the differential and Walsh spectra of $x^{2q+1}$ over $\mathbb{F}_{q^2}$

URL: http://arxiv.org/abs/2407.07710v2
Date: Sun, 27 Oct 2024 16:09:10 GMT
Title: On the differential and Walsh spectra of $x^{2q+1}$ over $\mathbb{F}_{q^2}$
Authors: Sihem Mesnager, Huawei Wu,
Abstract summary: We determine the differential spectrum of the power function $F(x)=x2q+1$ over $mathbbF_q2$. When the characteristic of $mathbbF_q2$ is $3$, we also determine the value distribution of the Walsh spectrum of $F$.
Score: 28.489574654566677
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Let $q$ be an odd prime power and let $\mathbb{F}_{q^2}$ be the finite field with $q^2$ elements. In this paper, we determine the differential spectrum of the power function $F(x)=x^{2q+1}$ over $\mathbb{F}_{q^2}$. When the characteristic of $\mathbb{F}_{q^2}$ is $3$, we also determine the value distribution of the Walsh spectrum of $F$, showing that it is $4$-valued, and use the obtained result to determine the weight distribution of a $4$-weight cyclic code.

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