Determining Sidon polynomials on Sidon sets over finite fields
DOI:
https://doi.org/10.13069/jacodesmath.v11i3.281Keywords:
Sidon sets, Planar polynomial, Finite fieldsAbstract
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 $\mathbb{F}_q\times \mathbb{F}_q$. In this paper, 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.
Received: 6 March 2023 | Accepted: 26 November 2023Downloads
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