Li Zhu

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20242026

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math.NT2026

The Optimal Coefficients-Based Criterion for Primitive Quadratic Polynomials over Finite Fields

Li Zhu, Hongfeng Wu

Let $F_{q}$ be a finite field and consider quadratic polynomials $f (X) = X^{2} + b X + c \in F_{q} [X]$ with primitive constant term $c$ . We construct an optimal coefficients-based…

math.NT2025

The Minimal Binomial Multiples of Polynomials over Finite Fields

Li Zhu, Hongfeng Wu

Let $f (X)$ be a nonconstant polynomial over $F_{q}$ , with a nonzero constant term. The order of $f (X)$ is a classical notion in the theory of polynomials over finite field…

math.NT2025

The Multiple Equal-Difference Structure of Cyclotomic Cosets

Li Zhu, Juncheng Zhou, Jinle Liu +1

In this paper we introduce the definition of equal-difference cyclotomic coset, and prove that in general any cyclotomic coset can be decomposed into a disjoint union of equal-diff…

math.NT2024

Explicit Representatives and Sizes of Cyclotomic Cosets II: Cyclotomic Systems and Applications to Constacyclic Codes

Li Zhu, Hongfeng Wu

Let $q = p^{e}$ be a prime power, let $ℓ$ be a prime with $g cd (ℓ, q n) = 1$ , and let $n$ be a positive integer. While $q$ -cyclotomic cosets are usually considered modulo a fixed int…