Shujun Zhao

collaborators

4 papers

math.NT2026

Classification of Rational Functions of Degree Three over Finite Fields

Xiang-dong Hou, Siyu Peng, Yongyu Qiang +1

We study rational functions over finite fields under PGL-equivalence. We say that $f, g \in F_{q} (X)$ are \emph{equivalent} if there exist $I ¨ , I ¨ \in F_{q} (X)$ of degree one…

math.NT2025

On Sum-Free Functions

Alyssa Ebeling, Xiang-dong Hou, Ashley Rydell +1

A function from $F_{2^{n}}$ to $F_{2^{n}}$ is said to be {\em $k$ th order sum-free} if the sum of its values over each $k$ -dimensional $F_{2}$ -affine subspace of $\Bbb F_{…

math.NT2025

On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function

Xiang-dong Hou, Shujun Zhao

A recent conjecture by C. Carlet on the sum-freedom of the binary multiplicative inverse function can be stated as follows: For each pair of positive integers $(n, k)$ with $3\le k\…

math.NT2025

Two Absolutely Irreducible Polynomials over $F_{2}$ and Their Applications to a Conjecture by Carlet

Xiang-dong Hou, Shujun Zhao

Two polynomials $F_{k} (X_{1}, \dots, X_{k})$ and $I^_{k} (X_{1}, \dots, X_{k})$ over $F_{2}$ arose from the study of a conjecture by C. Carlet about the sum-freedom of the multiplicative inverse…

Classification of Rational Functions of Degree Three over Finite Fields

On Sum-Free Functions

On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function

Two Absolutely Irreducible Polynomials over F2​ and Their Applications to a Conjecture by Carlet

Two Absolutely Irreducible Polynomials over $F_{2}$ and Their Applications to a Conjecture by Carlet