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arXiv · 2111.08886

Determining Sidon Polynomials on Sidon Sets over $\mathbb{F}_q\times \mathbb{F}_q$

Muhammad Afifurrahman·Aleams Barra
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Abstract

Let $p$ be a prime, and $q=p^n$ be a prime power. In his works on Sidon sets over $\mathbb{F}_q\times \mathbb{F}_q$, Cilleruelo conjectured about polynomials that could generate $q$-element Sidon sets over $\mathbb{F}_q\times \mathbb{F}_q$. Here, we derive some criteria for determining polynomials that could generate $q$-element Sidon set over $\mathbb{F}_q\times \mathbb{F}_q$. Using these criteria, we prove that certain classes of monomials and cubic polynomials over $\mathbb{F}_p$ cannot be used to generate $p$-element Sidon set over $\mathbb{F}_p\times \mathbb{F}_p$. We also discover a connection between the needed polynomials and planar polynomials.

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Muhammad Afifurrahman, Aleams Barra. 2021-11-17. Determining Sidon Polynomials on Sidon Sets over $\mathbb{F}_q\times \mathbb{F}_q$. https://doi.org/10.13069/jacodesmath.v11i3.281

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